R : Exploring and Visualizing Extracted Dimensions from Principal Component Algorithms
John Pauline Pineda
June 4, 2023
1. Table of Contents
This document explores methods in visualizing extracted dimensions from principal component algorithms using various helpful packages in R.
Dimensionality reduction is a form of unsupervised learning method aimed at reducing the number of features in a data set while retaining as much information as possible for purposes of lessening the complexity of the model, improving the performance of the learning algorithm or for formulating a more intuitive visualization of the data. The algorithms applied in this study (mostly contained in the factoextra, stats and FactoMineR packages) attempt to transform and project the data onto a lower-dimensional space while exploring visualization alternatives for the extracted dimensions.
1.1 Sample Data
The Oscars, Tomatometer and IMDB datasets obtained from the Kaggle website were used for this illustrated example.
Preliminary dataset assessment:
[A] 126 rows (observations)
[B] 19 columns (variables)
[B.1] 1/19 instance = Film variable (character)
[B.2] 1/19 labels = Year variable (factor)
[B.3] 1/19 labels = Picture variable (factor)
[B.3.1] Category 1 = Picture=WON
[B.3.2] Category 2 = Picture=NOM
[B.4] 16/19 descriptors = 8/16 numeric + 8/16 factor
[B.4.1] Tomatometer_Critic (numeric)
[B.4.2] Tomatometer_Audience (numeric)
[B.4.3] Tomatometer_Critic_Audience_Gap (numeric)
[B.4.4] IMDB_Critic (numeric)
[B.4.5] IMDB_Audience (numeric)
[B.4.6] IMDB_Critic_Audience_Gap (numeric)
[B.4.7] Nominations_Total (numeric)
[B.4.8] Nomination_SuccessRate (numeric)
[B.4.9] Genre (factor)
[B.4.10] Cinematography (factor)
[B.4.11] Directing (factor)
[B.4.12] Editing (factor)
[B.4.13] Screenplay (factor)
[B.4.14] Acting (factor)
[B.4.15] Design (factor)
[B.4.16] Sound (factor)
##################################
# Loading R libraries
##################################
library(AppliedPredictiveModeling)
library(caret)
library(rpart)
library(lattice)
library(dplyr)
library(tidyr)
library(moments)
library(skimr)
library(RANN)
library(pls)
library(corrplot)
library(tidyverse)
library(lares)
library(DMwR)
library(gridExtra)
library(rattle)
library(RColorBrewer)
library(stats)
library(factoextra)
library(FactoMineR)
library(gplots)
##################################
# Loading source and
# formulating the analysis set
##################################
Oscars <- read.csv("Oscars.csv",
na.strings=c("NA","NaN"," ",""),
stringsAsFactors = FALSE)
Oscars <- as.data.frame(Oscars)
##################################
# Performing a general exploration of the data set
##################################
dim(Oscars)## [1] 126 20str(Oscars)## 'data.frame': 126 obs. of 20 variables:
## $ Film : chr "Avatar" "The Blind Side" "District 9" "An Education" ...
## $ Year : int 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 ...
## $ Tomatometer_Critic : int 82 66 90 93 97 89 92 89 98 90 ...
## $ Tomatometer_Audience : int 82 85 82 80 84 88 74 68 90 79 ...
## $ Tomatometer_Critic_Audience_Gap: int 0 19 -8 -13 -13 -1 -18 -21 -8 -11 ...
## $ IMDB_Critic : int 83 53 81 85 95 69 78 88 88 83 ...
## $ IMDB_Audience : int 79 76 79 73 75 83 73 70 83 74 ...
## $ IMDB_Critic_Audience_Gap : int -4 23 -2 -12 -20 14 -5 -18 -5 -9 ...
## $ Nominations_Total : int 9 2 4 3 9 8 6 2 5 6 ...
## $ Nomination_SuccessRate : num 0.333 0.5 0 0 0.667 ...
## $ Genre : chr "Sci-Fi" "Biography" "Sci-Fi" "Drama" ...
## $ SideGenre : chr "Sci-Fi/Adventure" "Drama/Biography" "Sci-Fi/Mystery/Thriller" "Drama" ...
## $ Picture : chr "NOM" "NOM" "NOM" "NOM" ...
## $ Cinematography : chr "WON" "NNOM" "NNOM" "NNOM" ...
## $ Directing : chr "NOM" "NNOM" "NNOM" "NNOM" ...
## $ Editing : chr "NOM" "NNOM" "NOM" "NNOM" ...
## $ Screenplay : chr "NNOM" "NNOM" "NOM" "NOM" ...
## $ Acting : chr "NNOM" "WON" "NNOM" "NOM" ...
## $ Design : chr "WON" "NNOM" "NNOM" "NNOM" ...
## $ Sound : chr "NOM" "NNOM" "NNOM" "NNOM" ...summary(Oscars)## Film Year Tomatometer_Critic Tomatometer_Audience
## Length:126 Min. :2010 Min. :45.00 Min. :60.00
## Class :character 1st Qu.:2013 1st Qu.:87.00 1st Qu.:79.00
## Mode :character Median :2016 Median :92.00 Median :85.00
## Mean :2016 Mean :89.07 Mean :83.39
## 3rd Qu.:2020 3rd Qu.:95.00 3rd Qu.:90.00
## Max. :2023 Max. :99.00 Max. :99.00
## Tomatometer_Critic_Audience_Gap IMDB_Critic IMDB_Audience
## Min. :-25.000 Min. : 46.00 Min. :68.00
## 1st Qu.:-12.750 1st Qu.: 76.00 1st Qu.:74.00
## Median : -8.000 Median : 83.00 Median :77.00
## Mean : -5.683 Mean : 81.71 Mean :76.76
## 3rd Qu.: 0.000 3rd Qu.: 89.00 3rd Qu.:79.75
## Max. : 25.000 Max. :100.00 Max. :88.00
## IMDB_Critic_Audience_Gap Nominations_Total Nomination_SuccessRate
## Min. :-25.000 Min. : 2.000 Min. :0.0000
## 1st Qu.:-14.000 1st Qu.: 5.000 1st Qu.:0.0000
## Median : -7.000 Median : 6.000 Median :0.2000
## Mean : -4.952 Mean : 6.524 Mean :0.2362
## 3rd Qu.: 1.000 3rd Qu.: 8.000 3rd Qu.:0.3561
## Max. : 30.000 Max. :14.000 Max. :1.0000
## Genre SideGenre Picture Cinematography
## Length:126 Length:126 Length:126 Length:126
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
## Directing Editing Screenplay Acting
## Length:126 Length:126 Length:126 Length:126
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
## Design Sound
## Length:126 Length:126
## Class :character Class :character
## Mode :character Mode :character
##
##
## ##################################
# Transforming to appropriate data types
##################################
Oscars$Year <- factor(Oscars$Year,
levels = c("2010",
"2011",
"2012",
"2013",
"2014",
"2015",
"2016",
"2017",
"2018",
"2019",
"2020",
"2021",
"2022",
"2023"))
Oscars$Genre <- as.factor(Oscars$Genre)
Oscars$SideGenre <- as.factor(Oscars$SideGenre)
Oscars$Picture <- as.factor(Oscars$Picture)
Oscars$Cinematography <- as.factor(Oscars$Cinematography)
Oscars$Directing <- as.factor(Oscars$Directing)
Oscars$Editing <- as.factor(Oscars$Editing)
Oscars$Screenplay <- as.factor(Oscars$Screenplay)
Oscars$Acting <- as.factor(Oscars$Acting)
Oscars$Design <- as.factor(Oscars$Design)
Oscars$Sound <- as.factor(Oscars$Sound)
##################################
# Formulating a data type assessment summary
##################################
PDA <- Oscars
(PDA.Summary <- data.frame(
Column.Index=c(1:length(names(PDA))),
Column.Name= names(PDA),
Column.Type=sapply(PDA, function(x) class(x)),
row.names=NULL)
)## Column.Index Column.Name Column.Type
## 1 1 Film character
## 2 2 Year factor
## 3 3 Tomatometer_Critic integer
## 4 4 Tomatometer_Audience integer
## 5 5 Tomatometer_Critic_Audience_Gap integer
## 6 6 IMDB_Critic integer
## 7 7 IMDB_Audience integer
## 8 8 IMDB_Critic_Audience_Gap integer
## 9 9 Nominations_Total integer
## 10 10 Nomination_SuccessRate numeric
## 11 11 Genre factor
## 12 12 SideGenre factor
## 13 13 Picture factor
## 14 14 Cinematography factor
## 15 15 Directing factor
## 16 16 Editing factor
## 17 17 Screenplay factor
## 18 18 Acting factor
## 19 19 Design factor
## 20 20 Sound factor1.2 Data Quality Assessment
Data quality assessment:
[A] No missing observations noted for any variable.
[B] Low variance observed for 1 variable with First.Second.Mode.Ratio>5.
[B.1] Picture variable (factor)
[C] No low variance observed for any variable with Unique.Count.Ratio<0.01.
[D] No high skewness observed for any variable with Skewness>3 or Skewness<(-3).
[E] Considering the unsupervised learning nature of the analysis, no data pre-processing was proceeded to address the data quality issue identified.
##################################
# Loading dataset
##################################
DQA <- Oscars[,c(3:11,13:19)]
##################################
# Formulating an overall data quality assessment summary
##################################
(DQA.Summary <- data.frame(
Column.Index=c(1:length(names(DQA))),
Column.Name= names(DQA),
Column.Type=sapply(DQA, function(x) class(x)),
Row.Count=sapply(DQA, function(x) nrow(DQA)),
NA.Count=sapply(DQA,function(x)sum(is.na(x))),
Fill.Rate=sapply(DQA,function(x)format(round((sum(!is.na(x))/nrow(DQA)),3),nsmall=3)),
row.names=NULL)
)## Column.Index Column.Name Column.Type Row.Count NA.Count
## 1 1 Tomatometer_Critic integer 126 0
## 2 2 Tomatometer_Audience integer 126 0
## 3 3 Tomatometer_Critic_Audience_Gap integer 126 0
## 4 4 IMDB_Critic integer 126 0
## 5 5 IMDB_Audience integer 126 0
## 6 6 IMDB_Critic_Audience_Gap integer 126 0
## 7 7 Nominations_Total integer 126 0
## 8 8 Nomination_SuccessRate numeric 126 0
## 9 9 Genre factor 126 0
## 10 10 Picture factor 126 0
## 11 11 Cinematography factor 126 0
## 12 12 Directing factor 126 0
## 13 13 Editing factor 126 0
## 14 14 Screenplay factor 126 0
## 15 15 Acting factor 126 0
## 16 16 Design factor 126 0
## Fill.Rate
## 1 1.000
## 2 1.000
## 3 1.000
## 4 1.000
## 5 1.000
## 6 1.000
## 7 1.000
## 8 1.000
## 9 1.000
## 10 1.000
## 11 1.000
## 12 1.000
## 13 1.000
## 14 1.000
## 15 1.000
## 16 1.000##################################
# Listing all descriptors
##################################
DQA.Descriptors <- DQA
##################################
# Listing all numeric Descriptors
##################################
DQA.Descriptors.Numeric <- DQA.Descriptors[,sapply(DQA.Descriptors, is.numeric)]
if (length(names(DQA.Descriptors.Numeric))>0) {
print(paste0("There are ",
(length(names(DQA.Descriptors.Numeric))),
" numeric descriptor variable(s)."))
} else {
print("There are no numeric descriptor variables.")
}## [1] "There are 8 numeric descriptor variable(s)."##################################
# Listing all factor Descriptors
##################################
DQA.Descriptors.Factor <- DQA.Descriptors[,sapply(DQA.Descriptors, is.factor)]
if (length(names(DQA.Descriptors.Factor))>0) {
print(paste0("There are ",
(length(names(DQA.Descriptors.Factor))),
" factor descriptor variable(s)."))
} else {
print("There are no factor descriptor variables.")
}## [1] "There are 8 factor descriptor variable(s)."##################################
# Formulating a data quality assessment summary for factor Descriptors
##################################
if (length(names(DQA.Descriptors.Factor))>0) {
##################################
# Formulating a function to determine the first mode
##################################
FirstModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
ux[tab == max(tab)]
}
##################################
# Formulating a function to determine the second mode
##################################
SecondModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
fm = ux[tab == max(tab)]
sm = x[!(x %in% fm)]
usm <- unique(sm)
tabsm <- tabulate(match(sm, usm))
ifelse(is.na(usm[tabsm == max(tabsm)])==TRUE,
return("x"),
return(usm[tabsm == max(tabsm)]))
}
(DQA.Descriptors.Factor.Summary <- data.frame(
Column.Name= names(DQA.Descriptors.Factor),
Column.Type=sapply(DQA.Descriptors.Factor, function(x) class(x)),
Unique.Count=sapply(DQA.Descriptors.Factor, function(x) length(unique(x))),
First.Mode.Value=sapply(DQA.Descriptors.Factor, function(x) as.character(FirstModes(x)[1])),
Second.Mode.Value=sapply(DQA.Descriptors.Factor, function(x) as.character(SecondModes(x)[1])),
First.Mode.Count=sapply(DQA.Descriptors.Factor, function(x) sum(na.omit(x) == FirstModes(x)[1])),
Second.Mode.Count=sapply(DQA.Descriptors.Factor, function(x) sum(na.omit(x) == SecondModes(x)[1])),
Unique.Count.Ratio=sapply(DQA.Descriptors.Factor, function(x) format(round((length(unique(x))/nrow(DQA.Descriptors.Factor)),3), nsmall=3)),
First.Second.Mode.Ratio=sapply(DQA.Descriptors.Factor, function(x) format(round((sum(na.omit(x) == FirstModes(x)[1])/sum(na.omit(x) == SecondModes(x)[1])),3), nsmall=3)),
row.names=NULL)
)
}## Column.Name Column.Type Unique.Count First.Mode.Value Second.Mode.Value
## 1 Genre factor 16 Drama Comedy
## 2 Picture factor 2 NOM WON
## 3 Cinematography factor 3 NNOM NOM
## 4 Directing factor 3 NNOM NOM
## 5 Editing factor 3 NNOM NOM
## 6 Screenplay factor 3 NOM WON
## 7 Acting factor 3 NOM WON
## 8 Design factor 3 NNOM NOM
## First.Mode.Count Second.Mode.Count Unique.Count.Ratio First.Second.Mode.Ratio
## 1 25 22 0.127 1.136
## 2 112 14 0.016 8.000
## 3 80 33 0.024 2.424
## 4 59 53 0.024 1.113
## 5 61 52 0.024 1.173
## 6 73 28 0.024 2.607
## 7 55 40 0.024 1.375
## 8 82 32 0.024 2.562##################################
# Formulating a data quality assessment summary for numeric Descriptors
##################################
if (length(names(DQA.Descriptors.Numeric))>0) {
##################################
# Formulating a function to determine the first mode
##################################
FirstModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
ux[tab == max(tab)]
}
##################################
# Formulating a function to determine the second mode
##################################
SecondModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
fm = ux[tab == max(tab)]
sm = na.omit(x)[!(na.omit(x) %in% fm)]
usm <- unique(sm)
tabsm <- tabulate(match(sm, usm))
ifelse(is.na(usm[tabsm == max(tabsm)])==TRUE,
return(0.00001),
return(usm[tabsm == max(tabsm)]))
}
(DQA.Descriptors.Numeric.Summary <- data.frame(
Column.Name= names(DQA.Descriptors.Numeric),
Column.Type=sapply(DQA.Descriptors.Numeric, function(x) class(x)),
Unique.Count=sapply(DQA.Descriptors.Numeric, function(x) length(unique(x))),
Unique.Count.Ratio=sapply(DQA.Descriptors.Numeric, function(x) format(round((length(unique(x))/nrow(DQA.Descriptors.Numeric)),3), nsmall=3)),
First.Mode.Value=sapply(DQA.Descriptors.Numeric, function(x) format(round((FirstModes(x)[1]),3),nsmall=3)),
Second.Mode.Value=sapply(DQA.Descriptors.Numeric, function(x) format(round((SecondModes(x)[1]),3),nsmall=3)),
First.Mode.Count=sapply(DQA.Descriptors.Numeric, function(x) sum(na.omit(x) == FirstModes(x)[1])),
Second.Mode.Count=sapply(DQA.Descriptors.Numeric, function(x) sum(na.omit(x) == SecondModes(x)[1])),
First.Second.Mode.Ratio=sapply(DQA.Descriptors.Numeric, function(x) format(round((sum(na.omit(x) == FirstModes(x)[1])/sum(na.omit(x) == SecondModes(x)[1])),3), nsmall=3)),
Minimum=sapply(DQA.Descriptors.Numeric, function(x) format(round(min(x,na.rm = TRUE),3), nsmall=3)),
Mean=sapply(DQA.Descriptors.Numeric, function(x) format(round(mean(x,na.rm = TRUE),3), nsmall=3)),
Median=sapply(DQA.Descriptors.Numeric, function(x) format(round(median(x,na.rm = TRUE),3), nsmall=3)),
Maximum=sapply(DQA.Descriptors.Numeric, function(x) format(round(max(x,na.rm = TRUE),3), nsmall=3)),
Skewness=sapply(DQA.Descriptors.Numeric, function(x) format(round(skewness(x,na.rm = TRUE),3), nsmall=3)),
Kurtosis=sapply(DQA.Descriptors.Numeric, function(x) format(round(kurtosis(x,na.rm = TRUE),3), nsmall=3)),
Percentile25th=sapply(DQA.Descriptors.Numeric, function(x) format(round(quantile(x,probs=0.25,na.rm = TRUE),3), nsmall=3)),
Percentile75th=sapply(DQA.Descriptors.Numeric, function(x) format(round(quantile(x,probs=0.75,na.rm = TRUE),3), nsmall=3)),
row.names=NULL)
)
}## Column.Name Column.Type Unique.Count Unique.Count.Ratio
## 1 Tomatometer_Critic integer 31 0.246
## 2 Tomatometer_Audience integer 32 0.254
## 3 Tomatometer_Critic_Audience_Gap integer 41 0.325
## 4 IMDB_Critic integer 40 0.317
## 5 IMDB_Audience integer 19 0.151
## 6 IMDB_Critic_Audience_Gap integer 42 0.333
## 7 Nominations_Total integer 13 0.103
## 8 Nomination_SuccessRate numeric 26 0.206
## First.Mode.Value Second.Mode.Value First.Mode.Count Second.Mode.Count
## 1 93.000 90.000 11 10
## 2 90.000 91.000 9 8
## 3 -8.000 -10.000 10 8
## 4 88.000 81.000 10 9
## 5 77.000 78.000 13 12
## 6 -4.000 -5.000 7 5
## 7 6.000 4.000 31 17
## 8 0.000 0.333 35 12
## First.Second.Mode.Ratio Minimum Mean Median Maximum Skewness Kurtosis
## 1 1.100 45.000 89.071 92.000 99.000 -2.069 8.210
## 2 1.125 60.000 83.389 85.000 99.000 -0.751 3.359
## 3 1.250 -25.000 -5.683 -8.000 25.000 0.611 3.137
## 4 1.111 46.000 81.714 83.000 100.000 -1.019 4.101
## 5 1.083 68.000 76.762 77.000 88.000 0.019 2.761
## 6 1.400 -25.000 -4.952 -7.000 30.000 0.838 3.320
## 7 1.824 2.000 6.524 6.000 14.000 0.502 2.686
## 8 2.917 0.000 0.236 0.200 1.000 0.790 3.448
## Percentile25th Percentile75th
## 1 87.000 95.000
## 2 79.000 90.000
## 3 -12.750 0.000
## 4 76.000 89.000
## 5 74.000 79.750
## 6 -14.000 1.000
## 7 5.000 8.000
## 8 0.000 0.356##################################
# Identifying potential data quality issues
##################################
##################################
# Checking for missing observations
##################################
if ((nrow(DQA.Summary[DQA.Summary$NA.Count>0,]))>0){
print(paste0("Missing observations noted for ",
(nrow(DQA.Summary[DQA.Summary$NA.Count>0,])),
" variable(s) with NA.Count>0 and Fill.Rate<1.0."))
DQA.Summary[DQA.Summary$NA.Count>0,]
} else {
print("No missing observations noted.")
}## [1] "No missing observations noted."##################################
# Checking for zero or near-zero variance Descriptors
##################################
if (length(names(DQA.Descriptors.Factor))==0) {
print("No factor descriptors noted.")
} else if (nrow(DQA.Descriptors.Factor.Summary[as.numeric(as.character(DQA.Descriptors.Factor.Summary$First.Second.Mode.Ratio))>5,])>0){
print(paste0("Low variance observed for ",
(nrow(DQA.Descriptors.Factor.Summary[as.numeric(as.character(DQA.Descriptors.Factor.Summary$First.Second.Mode.Ratio))>5,])),
" factor variable(s) with First.Second.Mode.Ratio>5."))
DQA.Descriptors.Factor.Summary[as.numeric(as.character(DQA.Descriptors.Factor.Summary$First.Second.Mode.Ratio))>5,]
} else {
print("No low variance factor descriptors due to high first-second mode ratio noted.")
}## [1] "Low variance observed for 1 factor variable(s) with First.Second.Mode.Ratio>5."## Column.Name Column.Type Unique.Count First.Mode.Value Second.Mode.Value
## 2 Picture factor 2 NOM WON
## First.Mode.Count Second.Mode.Count Unique.Count.Ratio First.Second.Mode.Ratio
## 2 112 14 0.016 8.000if (length(names(DQA.Descriptors.Numeric))==0) {
print("No numeric descriptors noted.")
} else if (nrow(DQA.Descriptors.Numeric.Summary[as.numeric(as.character(DQA.Descriptors.Numeric.Summary$First.Second.Mode.Ratio))>5,])>0){
print(paste0("Low variance observed for ",
(nrow(DQA.Descriptors.Numeric.Summary[as.numeric(as.character(DQA.Descriptors.Numeric.Summary$First.Second.Mode.Ratio))>5,])),
" numeric variable(s) with First.Second.Mode.Ratio>5."))
DQA.Descriptors.Numeric.Summary[as.numeric(as.character(DQA.Descriptors.Numeric.Summary$First.Second.Mode.Ratio))>5,]
} else {
print("No low variance numeric descriptors due to high first-second mode ratio noted.")
}## [1] "No low variance numeric descriptors due to high first-second mode ratio noted."if (length(names(DQA.Descriptors.Numeric))==0) {
print("No numeric descriptors noted.")
} else if (nrow(DQA.Descriptors.Numeric.Summary[as.numeric(as.character(DQA.Descriptors.Numeric.Summary$Unique.Count.Ratio))<0.01,])>0){
print(paste0("Low variance observed for ",
(nrow(DQA.Descriptors.Numeric.Summary[as.numeric(as.character(DQA.Descriptors.Numeric.Summary$Unique.Count.Ratio))<0.01,])),
" numeric variable(s) with Unique.Count.Ratio<0.01."))
DQA.Descriptors.Numeric.Summary[as.numeric(as.character(DQA.Descriptors.Numeric.Summary$Unique.Count.Ratio))<0.01,]
} else {
print("No low variance numeric descriptors due to low unique count ratio noted.")
}## [1] "No low variance numeric descriptors due to low unique count ratio noted."##################################
# Checking for skewed Descriptors
##################################
if (length(names(DQA.Descriptors.Numeric))==0) {
print("No numeric descriptors noted.")
} else if (nrow(DQA.Descriptors.Numeric.Summary[as.numeric(as.character(DQA.Descriptors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Descriptors.Numeric.Summary$Skewness))<(-3),])>0){
print(paste0("High skewness observed for ",
(nrow(DQA.Descriptors.Numeric.Summary[as.numeric(as.character(DQA.Descriptors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Descriptors.Numeric.Summary$Skewness))<(-3),])),
" numeric variable(s) with Skewness>3 or Skewness<(-3)."))
DQA.Descriptors.Numeric.Summary[as.numeric(as.character(DQA.Descriptors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Descriptors.Numeric.Summary$Skewness))<(-3),]
} else {
print("No skewed numeric descriptors noted.")
}## [1] "No skewed numeric descriptors noted."1.3 Data Preprocessing
1.3.1 Dataset Formulation
Data Preparation:
[A] Different data formats and descriptor variables were considered depending on the dimensionality reduction method used in the analysis.
[B] Principal Component Analysis: Matrix data with the following variables:
[B.1] Row Labels : Film
[B.2] Quantitative PCA Descriptor: Tomatometer_Critic
[B.3] Quantitative PCA Descriptor: Tomatometer_Audience
[B.4] Quantitative PCA Descriptor: IMDB_Critic
[B.5] Quantitative PCA Descriptor: IMDB_Audience
[B.6] Quantitative PCA Descriptor: Nominations_Total
[B.7] Quantitative PCA Descriptor: Nomination_SuccessRate
[B.8] Post-PCA Factor: Year
[B.9] Post-PCA Factor: Picture
[C] Correspondence Analysis: Contingency table with the following variables:
[C.1] Qualitative CA Descriptor: Genre
[C.2] Qualitative CA Descriptor: Cinematography
[C.3] Qualitative CA Descriptor: Directing
[C.4] Qualitative CA Descriptor: Editing
[C.5] Qualitative CA Descriptor: Screenplay
[D] Multiple Correspondence Analysis: Matrix data with the following variables:
[D.1] Row Labels : Film
[D.2] Qualitative MCA Descriptor: Cinematography
[D.3] Qualitative MCA Descriptor: Directing
[D.4] Qualitative MCA Descriptor: Editing
[D.5] Qualitative MCA Descriptor: Screenplay
[D.6] Post-MCA Factor: Year
[D.7] Post-MCA Factor: Picture
[E] Multiple Factor Analysis: Matrix data with the following groups and variables:
[E.1] Row Labels: Film
[E.2] MFA Descriptor Group: Recognitions
[E.2.1] Quantitative MFA Descriptor: Nominations_Total
[E.2.2] Quantitative MFA Descriptor: Nomination_SuccessRate
[E.3] MFA Descriptor Group: Technicalities
[E.3.1] Qualitative MFA Descriptor: Picture
[E.3.2] Qualitative MFA Descriptor: Cinematography
[E.3.3] Qualitative MFA Descriptor: Directing
[E.4] MFA Descriptor Group : Storytelling
[E.4.1] Qualitative MFA Descriptor: Editing
[E.4.2] Qualitative MFA Descriptor: Screenplay
[E.4.3] Qualitative MFA Descriptor: Acting
[E.5] MFA Descriptor Group : Aesthetics
[E.5.1] Qualitative MFA Descriptor: Design
[E.5.2] Qualitative MFA Descriptor: Sound
[F] Factor Analysis of Mixed Data: Matrix data with the following variables:
[F.1] Row Labels : Film
[F.2] Quantitative FAMD Descriptor: Tomatometer_Critic
[F.3] Quantitative FAMD Descriptor: Tomatometer_Audience
[F.4] Qualitative FAMD Descriptor: Picture
[F.5] Qualitative FAMD Descriptor: Cinematography
[F.6] Qualitative FAMD Descriptor: Directing
[F.7] Qualitative FAMD Descriptor: Editing
[F.8] Qualitative FAMD Descriptor: Screenplay
##################################
# Formulating dataset versions
# for the different principal component algorithms
##################################
##################################
# Formulating dataset for
# Principal Component Analysis
##################################
Oscars.PCA <- Oscars[,c("Tomatometer_Critic",
"Tomatometer_Audience",
"IMDB_Critic",
"IMDB_Audience",
"Nominations_Total",
"Nomination_SuccessRate",
"Year",
"Picture")]
row.names(Oscars.PCA) <- Oscars$Film
dim(Oscars.PCA)## [1] 126 8str(Oscars.PCA)## 'data.frame': 126 obs. of 8 variables:
## $ Tomatometer_Critic : int 82 66 90 93 97 89 92 89 98 90 ...
## $ Tomatometer_Audience : int 82 85 82 80 84 88 74 68 90 79 ...
## $ IMDB_Critic : int 83 53 81 85 95 69 78 88 88 83 ...
## $ IMDB_Audience : int 79 76 79 73 75 83 73 70 83 74 ...
## $ Nominations_Total : int 9 2 4 3 9 8 6 2 5 6 ...
## $ Nomination_SuccessRate: num 0.333 0.5 0 0 0.667 ...
## $ Year : Factor w/ 14 levels "2010","2011",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Picture : Factor w/ 2 levels "NOM","WON": 1 1 1 1 2 1 1 1 1 1 ...summary(Oscars.PCA)## Tomatometer_Critic Tomatometer_Audience IMDB_Critic IMDB_Audience
## Min. :45.00 Min. :60.00 Min. : 46.00 Min. :68.00
## 1st Qu.:87.00 1st Qu.:79.00 1st Qu.: 76.00 1st Qu.:74.00
## Median :92.00 Median :85.00 Median : 83.00 Median :77.00
## Mean :89.07 Mean :83.39 Mean : 81.71 Mean :76.76
## 3rd Qu.:95.00 3rd Qu.:90.00 3rd Qu.: 89.00 3rd Qu.:79.75
## Max. :99.00 Max. :99.00 Max. :100.00 Max. :88.00
##
## Nominations_Total Nomination_SuccessRate Year Picture
## Min. : 2.000 Min. :0.0000 2010 :10 NOM:112
## 1st Qu.: 5.000 1st Qu.:0.0000 2011 :10 WON: 14
## Median : 6.000 Median :0.2000 2022 :10
## Mean : 6.524 Mean :0.2362 2023 :10
## 3rd Qu.: 8.000 3rd Qu.:0.3561 2012 : 9
## Max. :14.000 Max. :1.0000 2013 : 9
## (Other):68##################################
# Formulating dataset for
# Correspondence Analysis
##################################
Oscars.CA.Cinematography <- Oscars[,c("Genre",
"Cinematography")]
(Oscars.CA.Cinematography <- as.data.frame.matrix(
table(Oscars.CA.Cinematography$Genre,Oscars.CA.Cinematography$Cinematography)))## NNOM NOM WON
## Action 3 1 0
## Adventure 1 0 2
## Biography 8 3 1
## Comedy 17 4 1
## Crime 3 2 0
## Drama 22 2 1
## Family 2 0 0
## History 8 6 0
## LGBTQ+ 2 1 0
## Music 2 1 0
## Musical 1 1 1
## Romance 3 2 0
## Sci-Fi 3 2 4
## Thriller 4 2 0
## War 1 3 2
## Western 0 3 1Oscars.CA.Directing <- Oscars[,c("Genre",
"Directing")]
(Oscars.CA.Directing <- as.data.frame.matrix(
table(Oscars.CA.Directing$Genre,Oscars.CA.Directing$Directing)))## NNOM NOM WON
## Action 3 1 0
## Adventure 0 2 1
## Biography 8 4 0
## Comedy 6 14 2
## Crime 2 3 0
## Drama 12 11 2
## Family 2 0 0
## History 10 3 1
## LGBTQ+ 2 1 0
## Music 2 1 0
## Musical 1 1 1
## Romance 2 2 1
## Sci-Fi 5 2 2
## Thriller 2 3 1
## War 1 4 1
## Western 1 1 2Oscars.CA.Editing <- Oscars[,c("Genre",
"Editing")]
(Oscars.CA.Editing <- as.data.frame.matrix(
table(Oscars.CA.Editing$Genre,Oscars.CA.Editing$Editing)))## NNOM NOM WON
## Action 1 2 1
## Adventure 1 2 0
## Biography 4 6 2
## Comedy 11 10 1
## Crime 0 5 0
## Drama 19 6 0
## Family 2 0 0
## History 7 5 2
## LGBTQ+ 1 2 0
## Music 0 1 2
## Musical 2 1 0
## Romance 4 1 0
## Sci-Fi 3 4 2
## Thriller 2 4 0
## War 2 1 3
## Western 2 2 0Oscars.CA.Screenplay <- Oscars[,c("Genre",
"Screenplay")]
(Oscars.CA.Screenplay <- as.data.frame.matrix(
table(Oscars.CA.Screenplay$Genre,Oscars.CA.Screenplay$Screenplay)))## NNOM NOM WON
## Action 2 2 0
## Adventure 0 3 0
## Biography 4 7 1
## Comedy 0 14 8
## Crime 0 5 0
## Drama 3 15 7
## Family 0 2 0
## History 5 5 4
## LGBTQ+ 0 1 2
## Music 0 3 0
## Musical 2 1 0
## Romance 1 3 1
## Sci-Fi 3 6 0
## Thriller 2 1 3
## War 2 3 1
## Western 1 2 1##################################
# Formulating dataset for
# Multiple Correspondence Analysis
##################################
Oscars.MCA <- Oscars[,c("Cinematography",
"Directing",
"Editing",
"Screenplay",
"Year",
"Picture")]
row.names(Oscars.MCA) <- Oscars$Film
dim(Oscars.MCA)## [1] 126 6str(Oscars.MCA)## 'data.frame': 126 obs. of 6 variables:
## $ Cinematography: Factor w/ 3 levels "NNOM","NOM","WON": 3 1 1 1 2 2 1 1 1 1 ...
## $ Directing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 1 1 3 2 2 1 1 2 ...
## $ Editing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 2 1 3 2 2 1 1 1 ...
## $ Screenplay : Factor w/ 3 levels "NNOM","NOM","WON": 1 1 2 2 3 2 3 2 2 2 ...
## $ Year : Factor w/ 14 levels "2010","2011",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Picture : Factor w/ 2 levels "NOM","WON": 1 1 1 1 2 1 1 1 1 1 ...summary(Oscars.MCA)## Cinematography Directing Editing Screenplay Year Picture
## NNOM:80 NNOM:59 NNOM:61 NNOM:25 2010 :10 NOM:112
## NOM :33 NOM :53 NOM :52 NOM :73 2011 :10 WON: 14
## WON :13 WON :14 WON :13 WON :28 2022 :10
## 2023 :10
## 2012 : 9
## 2013 : 9
## (Other):68##################################
# Formulating dataset for
# Multiple Factor Analysis
##################################
Oscars.MFA <- Oscars[,c("Nominations_Total",
"Nomination_SuccessRate",
"Picture",
"Cinematography",
"Directing",
"Editing",
"Screenplay",
"Acting",
"Design",
"Sound")]
row.names(Oscars.MFA) <- Oscars$Film
dim(Oscars.MFA)## [1] 126 10str(Oscars.MFA)## 'data.frame': 126 obs. of 10 variables:
## $ Nominations_Total : int 9 2 4 3 9 8 6 2 5 6 ...
## $ Nomination_SuccessRate: num 0.333 0.5 0 0 0.667 ...
## $ Picture : Factor w/ 2 levels "NOM","WON": 1 1 1 1 2 1 1 1 1 1 ...
## $ Cinematography : Factor w/ 3 levels "NNOM","NOM","WON": 3 1 1 1 2 2 1 1 1 1 ...
## $ Directing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 1 1 3 2 2 1 1 2 ...
## $ Editing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 2 1 3 2 2 1 1 1 ...
## $ Screenplay : Factor w/ 3 levels "NNOM","NOM","WON": 1 1 2 2 3 2 3 2 2 2 ...
## $ Acting : Factor w/ 3 levels "NNOM","NOM","WON": 1 3 1 2 2 3 3 1 1 2 ...
## $ Design : Factor w/ 3 levels "NNOM","NOM","WON": 3 1 1 1 1 1 1 1 1 1 ...
## $ Sound : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 1 1 3 2 1 1 2 1 ...summary(Oscars.MFA)## Nominations_Total Nomination_SuccessRate Picture Cinematography Directing
## Min. : 2.000 Min. :0.0000 NOM:112 NNOM:80 NNOM:59
## 1st Qu.: 5.000 1st Qu.:0.0000 WON: 14 NOM :33 NOM :53
## Median : 6.000 Median :0.2000 WON :13 WON :14
## Mean : 6.524 Mean :0.2362
## 3rd Qu.: 8.000 3rd Qu.:0.3561
## Max. :14.000 Max. :1.0000
## Editing Screenplay Acting Design Sound
## NNOM:61 NNOM:25 NNOM:31 NNOM:82 NNOM:76
## NOM :52 NOM :73 NOM :55 NOM :32 NOM :34
## WON :13 WON :28 WON :40 WON :12 WON :16
##
##
## ##################################
# Formulating dataset for
# Factor Analysis of Mixed Data
##################################
Oscars.FAMD <- Oscars[,c("Nominations_Total",
"Nomination_SuccessRate",
"Picture",
"Cinematography",
"Directing",
"Editing",
"Screenplay")]
row.names(Oscars.FAMD) <- Oscars$Film
dim(Oscars.FAMD)## [1] 126 7str(Oscars.FAMD)## 'data.frame': 126 obs. of 7 variables:
## $ Nominations_Total : int 9 2 4 3 9 8 6 2 5 6 ...
## $ Nomination_SuccessRate: num 0.333 0.5 0 0 0.667 ...
## $ Picture : Factor w/ 2 levels "NOM","WON": 1 1 1 1 2 1 1 1 1 1 ...
## $ Cinematography : Factor w/ 3 levels "NNOM","NOM","WON": 3 1 1 1 2 2 1 1 1 1 ...
## $ Directing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 1 1 3 2 2 1 1 2 ...
## $ Editing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 2 1 3 2 2 1 1 1 ...
## $ Screenplay : Factor w/ 3 levels "NNOM","NOM","WON": 1 1 2 2 3 2 3 2 2 2 ...summary(Oscars.FAMD)## Nominations_Total Nomination_SuccessRate Picture Cinematography Directing
## Min. : 2.000 Min. :0.0000 NOM:112 NNOM:80 NNOM:59
## 1st Qu.: 5.000 1st Qu.:0.0000 WON: 14 NOM :33 NOM :53
## Median : 6.000 Median :0.2000 WON :13 WON :14
## Mean : 6.524 Mean :0.2362
## 3rd Qu.: 8.000 3rd Qu.:0.3561
## Max. :14.000 Max. :1.0000
## Editing Screenplay
## NNOM:61 NNOM:25
## NOM :52 NOM :73
## WON :13 WON :28
##
##
## 1.4 Data Exploration
Exploratory data analysis:
[A] Critic and audience scores including their gaps from both sources were correlated.
[A.1] High Tomatometer_Critic = High IMDB_Critic
[A.2] High Tomatometer_Audience = High IMDB_Audience
[A.3] Low Tomatometer_Critic_Audience_Gap = Low IMDB_Critic_Audience_Gap
[B] Movies which won the best picture award generally had the following characteristics:
[B.1] High Tomatometer_Critic and IMDB_Critic scores
[B.2] High Tomatometer_Audience and IMDB_Audience scores
[B.3] Low Tomatometer_Critic_Audience_Gap and IMDB_Critic_Audience_Gap scores
[B.4] High Nominations_Total and Nomination_SuccessRate scores
[B.5] Winners for the Directing and Screenplay categories
##################################
# Loading dataset
##################################
EDA_Oscars <- Oscars
str(EDA_Oscars)## 'data.frame': 126 obs. of 20 variables:
## $ Film : chr "Avatar" "The Blind Side" "District 9" "An Education" ...
## $ Year : Factor w/ 14 levels "2010","2011",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Tomatometer_Critic : int 82 66 90 93 97 89 92 89 98 90 ...
## $ Tomatometer_Audience : int 82 85 82 80 84 88 74 68 90 79 ...
## $ Tomatometer_Critic_Audience_Gap: int 0 19 -8 -13 -13 -1 -18 -21 -8 -11 ...
## $ IMDB_Critic : int 83 53 81 85 95 69 78 88 88 83 ...
## $ IMDB_Audience : int 79 76 79 73 75 83 73 70 83 74 ...
## $ IMDB_Critic_Audience_Gap : int -4 23 -2 -12 -20 14 -5 -18 -5 -9 ...
## $ Nominations_Total : int 9 2 4 3 9 8 6 2 5 6 ...
## $ Nomination_SuccessRate : num 0.333 0.5 0 0 0.667 ...
## $ Genre : Factor w/ 16 levels "Action","Adventure",..: 13 3 13 6 15 15 6 4 7 4 ...
## $ SideGenre : Factor w/ 32 levels "Action/Adventure",..: 25 13 27 12 30 29 12 9 17 9 ...
## $ Picture : Factor w/ 2 levels "NOM","WON": 1 1 1 1 2 1 1 1 1 1 ...
## $ Cinematography : Factor w/ 3 levels "NNOM","NOM","WON": 3 1 1 1 2 2 1 1 1 1 ...
## $ Directing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 1 1 3 2 2 1 1 2 ...
## $ Editing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 2 1 3 2 2 1 1 1 ...
## $ Screenplay : Factor w/ 3 levels "NNOM","NOM","WON": 1 1 2 2 3 2 3 2 2 2 ...
## $ Acting : Factor w/ 3 levels "NNOM","NOM","WON": 1 3 1 2 2 3 3 1 1 2 ...
## $ Design : Factor w/ 3 levels "NNOM","NOM","WON": 3 1 1 1 1 1 1 1 1 1 ...
## $ Sound : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 1 1 3 2 1 1 2 1 ...##################################
# Exploratory analysis
# among quantitative descriptors
# grouped by Picture
##################################
splom(~EDA_Oscars[,c(3:10)],
groups = EDA_Oscars$Picture,
pch = 16,
cex = 1,
alpha = 0.45,
varnames = c("T_CTC", "T_AUD", "T_GAP",
"I_CTC", "I_AUD", "I_GAP",
"NOM", "WIN%"),
auto.key = list(points = TRUE, space = "right"),
main = "Exploratory Analysis Between Picture and Quantitative Descriptors",
xlab = "Scatterplot Matrix of Quantitative Descriptors")
##################################
# Exploratory analysis
# among quantitative descriptors
# grouped by Year
##################################
splom(~EDA_Oscars[,c(3:10)],
groups = EDA_Oscars$Year,
pch = 16,
cex = 1,
alpha = 0.45,
varnames = c("T_CTC", "T_AUD", "T_GAP",
"I_CTC", "I_AUD", "I_GAP",
"NOM", "WIN%"),
auto.key = list(points = TRUE, space = "right"),
main = "Exploratory Analysis Between Year and Quantitative Descriptors",
xlab = "Scatterplot Matrix of Quantitative Descriptors")
##################################
# Exploratory analysis
# among qualitative descriptors
# grouped by Picture
##################################
##################################
# Creating a function to formulate
# the proportions table
##################################
EDA.PropTable.Function <- function(FactorVar) {
EDA.Bar.Source.FactorVar <- EDA_Oscars[,c("Picture",
FactorVar)]
EDA.Bar.Source.FactorVar.Prop <- as.data.frame(prop.table(table(EDA.Bar.Source.FactorVar), 2))
names(EDA.Bar.Source.FactorVar.Prop)[2] <- "Status"
EDA.Bar.Source.FactorVar.Prop$Variable <- rep(FactorVar,nrow(EDA.Bar.Source.FactorVar.Prop))
return(EDA.Bar.Source.FactorVar.Prop)
}
(EDA.Bar.Source.FactorVar.Prop <- rbind(EDA.PropTable.Function(names(EDA_Oscars)[14]),
EDA.PropTable.Function(names(EDA_Oscars)[15]),
EDA.PropTable.Function(names(EDA_Oscars)[16]),
EDA.PropTable.Function(names(EDA_Oscars)[17]),
EDA.PropTable.Function(names(EDA_Oscars)[18]),
EDA.PropTable.Function(names(EDA_Oscars)[19]),
EDA.PropTable.Function(names(EDA_Oscars)[20])))## Picture Status Freq Variable
## 1 NOM NNOM 0.91250000 Cinematography
## 2 WON NNOM 0.08750000 Cinematography
## 3 NOM NOM 0.81818182 Cinematography
## 4 WON NOM 0.18181818 Cinematography
## 5 NOM WON 0.92307692 Cinematography
## 6 WON WON 0.07692308 Cinematography
## 7 NOM NNOM 0.94915254 Directing
## 8 WON NNOM 0.05084746 Directing
## 9 NOM NOM 0.94339623 Directing
## 10 WON NOM 0.05660377 Directing
## 11 NOM WON 0.42857143 Directing
## 12 WON WON 0.57142857 Directing
## 13 NOM NNOM 0.96721311 Editing
## 14 WON NNOM 0.03278689 Editing
## 15 NOM NOM 0.82692308 Editing
## 16 WON NOM 0.17307692 Editing
## 17 NOM WON 0.76923077 Editing
## 18 WON WON 0.23076923 Editing
## 19 NOM NNOM 1.00000000 Screenplay
## 20 WON NNOM 0.00000000 Screenplay
## 21 NOM NOM 0.95890411 Screenplay
## 22 WON NOM 0.04109589 Screenplay
## 23 NOM WON 0.60714286 Screenplay
## 24 WON WON 0.39285714 Screenplay
## 25 NOM NNOM 0.96774194 Acting
## 26 WON NNOM 0.03225806 Acting
## 27 NOM NOM 0.90909091 Acting
## 28 WON NOM 0.09090909 Acting
## 29 NOM WON 0.80000000 Acting
## 30 WON WON 0.20000000 Acting
## 31 NOM NNOM 0.89024390 Design
## 32 WON NNOM 0.10975610 Design
## 33 NOM NOM 0.87500000 Design
## 34 WON NOM 0.12500000 Design
## 35 NOM WON 0.91666667 Design
## 36 WON WON 0.08333333 Design
## 37 NOM NNOM 0.88157895 Sound
## 38 WON NNOM 0.11842105 Sound
## 39 NOM NOM 0.88235294 Sound
## 40 WON NOM 0.11764706 Sound
## 41 NOM WON 0.93750000 Sound
## 42 WON WON 0.06250000 Sound(EDA.Barchart.FactorVar <- barchart(EDA.Bar.Source.FactorVar.Prop[,3] ~
EDA.Bar.Source.FactorVar.Prop[,2] |
EDA.Bar.Source.FactorVar.Prop[,4],
data=EDA.Bar.Source.FactorVar.Prop,
groups = EDA.Bar.Source.FactorVar.Prop[,1],
stack=TRUE,
ylab = "Proportion",
layout=(c(3,3)),
auto.key = list(points = TRUE, space = "right"),
main = "Exploratory Analysis Between Picture and Qualitative Descriptors",
xlab = "Bar Chart of Qualitative Descriptors"))
1.5 Dimensionality Reduction
1.5.1 Principal Component Analysis (PCA)
Principal Component Analysis employs a linear transformation that is based on preserving the most variance in the data using the least number of dimensions. The original data set in a higher dimensional space is mapped to a lower dimension space with maximum variance. The process involves the construction of the covariance matrix of the original data set. The eigenvectors of the covariance matrix of the data are referred to as principal axes, and the projection of the data instances on to these principal axes are called the principal components. Dimensionality reduction is obtained by only retaining the axes (dimensions) that account for most of the variance, and discarding all others.
[A] The percentage contributions for each principal component derived from the analysis in explaining the variance in the dataset are given as follows:
[A.1] PC1 = 37%
[A.2] Combined PC1 and PC2 = 65%
[A.3] Combined PC1, PC2 and PC3 = 82%
[B] With eigenvalues sufficiently greater than 1, only PC1 and PC2 were used in the subsequent exploratory analysis.
[B.1] PC1 = 2.22
[B.1] PC2 = 1.67
[C] PC1 can be described as having a collectively high or low critic and audience scores, oscar nominations and oscar winnability rate, as characterized by the following descriptor variables, ranked based on contribution and statistical significance:
[C.1] High Tomatometer_Critic = 23.09%
[C.2] High IMDB_Audience = 22.92%
[C.3] High Tomatometer_Audience = 19.56%
[C.4] High IMDB_Critic = 14.87%
[C.5] High Nomination_SuccessRate = 13.73%
[C.6] High Nominations_Total = 5.82%
[D] PC2 can be described as having high critic scores but low audience scores and oscar winnability rate, or having low critic scores but high audience scores and oscar winnability rate, as characterized by the following descriptor variables, ranked based on importance and statistical significance:
[D.1] High IMDB_Critic = 36.44%
[D.2] High Tomatometer_Critic = 22.50%
[D.3] Low IMDB_Audience = 16.37%
[D.4] Low Tomatometer_Audience = 15.68%
[D.5] Low Nomination_SuccessRate = 8.54%
[E] With both PC1 and PC2 considered,the following relationships were observed among descriptor variables:
[E.1] Critic and audience scores are the most represented descriptor variables for both principal components.
[E.1.1] IMDB_Critic
[E.1.2] Tomatometer_Critic
[E.1.3] IMDB_Audience
[E.1.4] Tomatometer_Audience
[E.2] Descriptor variables demonstrated correlation and clustered around three groups:
[E.2.1] Cluster 1 (IMDB_Critic, Tomatometer_Critic) indicates that critic scores are consistent for both sources (Tomatometer and IMDB).
[E.2.2] Cluster 2 (IMDB_Audience, Tomatometer_Audience, Nomination_SuccessRate) indicates that audience scores are consistent for both sources (Tomatometer and IMDB) and are positively correlated with oscar winnability rate.
[E.2.3] Cluster 3 (Nominations_Total) indicates that the number of oscar nominations is not correlated with critic and audience scores, as well as oscar winnability rate.
[F] With both PC1 and PC2 considered,the following relationships were observed among individual instances:
[F.1] Movies which won the oscar best picture award (e.g. Parasite, The King’s Speech, 12 Years a Slave, Spotlight, The Artist, Argo, The Hurt Locker and Everything Everywhere All At Once) generally had higher critic scores, audience scores, oscar nominations and oscar winnability rate, than those movies which were not given such an award. Other movie nominees which had the same characteristics included Toy Story 3, The Grand Budapest Hotel, The Father, La La Land, Gravity and Up.
[F.2] Other Movies which won the oscar best picture award (e.g. Moonlight and The Shape of Water) had higher critic scores but generally lower audience scores. Other movie nominees which had the same characteristics included Roma, Boyhood, Drive My Car, The Irishman, Minari and Manchester by the Sea.
[F.3] Other Movies which won the oscar best picture award (e.g. Green Book and CODA) had higher audience scores but generally lower critic scores. Other movie nominees which had the same characteristics included Inception, Dune, Top Gun: Maverick, Django Unchaied, Ford V Ferrari and Dallas Buyers Club.
[F.4] Movie nominees which had both generally lower critic and audience scores including Extremely Loud & Incredibly Close, Don’t Look Up, Vice and Triangle of Sadness highly contributed the variances captured by PC1. Movie nominees which had had extremely lower critic scores but reasonably audience scores including Bohemian Rhapsody, The Blind Side and Joker highly contributed the variances captured by PC2.
[F.5] There is no clear pattern in characteristics when movies are grouped by the year of release.
##################################
# Loading dataset
##################################
SD_PCA <- Oscars.PCA
str(SD_PCA)## 'data.frame': 126 obs. of 8 variables:
## $ Tomatometer_Critic : int 82 66 90 93 97 89 92 89 98 90 ...
## $ Tomatometer_Audience : int 82 85 82 80 84 88 74 68 90 79 ...
## $ IMDB_Critic : int 83 53 81 85 95 69 78 88 88 83 ...
## $ IMDB_Audience : int 79 76 79 73 75 83 73 70 83 74 ...
## $ Nominations_Total : int 9 2 4 3 9 8 6 2 5 6 ...
## $ Nomination_SuccessRate: num 0.333 0.5 0 0 0.667 ...
## $ Year : Factor w/ 14 levels "2010","2011",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Picture : Factor w/ 2 levels "NOM","WON": 1 1 1 1 2 1 1 1 1 1 ...##################################
# Performing PCA
##################################
DR_PCA <- PCA(SD_PCA[,c(1:6)],
scale.unit = TRUE,
graph = FALSE)
##################################
# Obtaining the PCA eigenvalues
##################################
(DR_PCA_EV <- get_eigenvalue(DR_PCA))## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 2.21987218 36.997870 36.99787
## Dim.2 1.66513612 27.752269 64.75014
## Dim.3 1.01373817 16.895636 81.64577
## Dim.4 0.67604616 11.267436 92.91321
## Dim.5 0.33051908 5.508651 98.42186
## Dim.6 0.09468828 1.578138 100.00000##################################
# Formulating the Scree Plot
# for the variances
##################################
(DR_PCA_VarianceScreePlot <- fviz_eig(DR_PCA,
addlabels = TRUE,
ylim = c(0, 100),
choice = c("variance")) +
labs(title = "Principal Component Analysis : Scree Plot of Explained Variances",
subtitle = "Top 2 Principal Components",
y = "Percentage of Explained Variances",
x = "Principal Components") +
theme_classic())
##################################
# Formulating the Scree Plot
# for the eigenvalues
##################################
(DR_PCA_EigenvalueScreePlot <- fviz_eig(DR_PCA,
addlabels = TRUE,
ylim = c(0, 6),
choice = c("eigenvalue")) +
labs(title = "Principal Component Analysis : Scree Plot of Eigenvalues",
subtitle = "Top 2 Principal Components",
y = "Eigenvalues",
x = "Principal Components") +
theme_classic())
##################################
# Extracting the PCA
# descriptor variable loadings
##################################
DR_PCA_VAR <- get_pca_var(DR_PCA)
##################################
# Extracting the coordinates
# representing the loadings
# for the descriptor variables
##################################
DR_PCA_VAR$coord## Dim.1 Dim.2 Dim.3 Dim.4
## Tomatometer_Critic 0.7160011 0.61208661 -0.24062432 -0.01481838
## Tomatometer_Audience 0.6589988 -0.51101999 -0.35527700 0.23993434
## IMDB_Critic 0.5746051 0.77898937 -0.03684305 -0.06857649
## IMDB_Audience 0.7133572 -0.52207446 -0.07046626 0.19067464
## Nominations_Total 0.3594166 0.08771218 0.85255162 0.35355795
## Nomination_SuccessRate 0.5520012 -0.37718042 0.31056271 -0.67245470
## Dim.5
## Tomatometer_Critic 0.10911558
## Tomatometer_Audience 0.33343405
## IMDB_Critic -0.12768134
## IMDB_Audience -0.41907508
## Nominations_Total 0.10547110
## Nomination_SuccessRate 0.06621183##################################
# Extracting the correlations
# between the descriptor variables
# and principal component dimensions
##################################
DR_PCA_VAR$cor## Dim.1 Dim.2 Dim.3 Dim.4
## Tomatometer_Critic 0.7160011 0.61208661 -0.24062432 -0.01481838
## Tomatometer_Audience 0.6589988 -0.51101999 -0.35527700 0.23993434
## IMDB_Critic 0.5746051 0.77898937 -0.03684305 -0.06857649
## IMDB_Audience 0.7133572 -0.52207446 -0.07046626 0.19067464
## Nominations_Total 0.3594166 0.08771218 0.85255162 0.35355795
## Nomination_SuccessRate 0.5520012 -0.37718042 0.31056271 -0.67245470
## Dim.5
## Tomatometer_Critic 0.10911558
## Tomatometer_Audience 0.33343405
## IMDB_Critic -0.12768134
## IMDB_Audience -0.41907508
## Nominations_Total 0.10547110
## Nomination_SuccessRate 0.06621183##################################
# Extracting the quality of representation
# for the descriptor variables
# on the factor map
##################################
DR_PCA_VAR$cos2## Dim.1 Dim.2 Dim.3 Dim.4
## Tomatometer_Critic 0.5126576 0.374650014 0.057900065 0.0002195845
## Tomatometer_Audience 0.4342794 0.261141435 0.126221744 0.0575684853
## IMDB_Critic 0.3301711 0.606824433 0.001357411 0.0047027343
## IMDB_Audience 0.5088785 0.272561741 0.004965494 0.0363568172
## Nominations_Total 0.1291803 0.007693427 0.726844261 0.1250032235
## Nomination_SuccessRate 0.3047053 0.142265072 0.096449197 0.4521953177
## Dim.5
## Tomatometer_Critic 0.011906210
## Tomatometer_Audience 0.111178264
## IMDB_Critic 0.016302526
## IMDB_Audience 0.175623921
## Nominations_Total 0.011124154
## Nomination_SuccessRate 0.004384007##################################
# Extracting the contributions
# (in percentage) of the descriptor variables
# to the principal components
##################################
DR_PCA_VAR$contrib## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Tomatometer_Critic 23.094013 22.4996629 5.7115404 0.03248069 3.602276
## Tomatometer_Audience 19.563262 15.6828881 12.4511188 8.51546661 33.637472
## IMDB_Critic 14.873427 36.4429325 0.1339015 0.69562326 4.932401
## IMDB_Audience 22.923776 16.3687363 0.4898202 5.37786015 53.135789
## Nominations_Total 5.819268 0.4620299 71.6994072 18.49033844 3.365662
## Nomination_SuccessRate 13.726255 8.5437503 9.5142118 66.88823084 1.326400##################################
# Extracting the quality of representation
# for the descriptor variables
# on the factor map
##################################
(DR_PCA_VariableSquaredCorrelationCircle <- fviz_pca_var(DR_PCA,
col.var = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
legend.title = "Squared Coordinates") +
labs(title = "Principal Component Analysis : Squared Coordinate Plot",
subtitle = "Descriptor Variable Representation Quality",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Formulating clusters of the
# descriptor variables
##################################
set.seed(123)
DR_PCA_KMEANS <- kmeans(DR_PCA_VAR$coord, centers=3, nstart=25)
DR_PCA_KMEANS_CLUSTER <- as.factor(DR_PCA_KMEANS$cluster)
##################################
# Extracting the correlation
# between the descriptor variables
# and top principal components
##################################
(DR_PCA_VariableCorrelationCircle <- fviz_pca_var(DR_PCA,
col.var = DR_PCA_KMEANS_CLUSTER,
palette = c("#0073C2FF", "#EFC000FF", "#868686FF"),
legend.title = "Cluster") +
labs(title = "Principal Component Analysis : Correlation Plot of Quantitative Variables",
subtitle = "Principal Components Versus Descriptor Variable Clusters",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Extracting the contribution
# of the descriptor variables
# for the the Top 1 and 2 principal components
##################################
(DR_PCA_PCVariableContributors <- fviz_contrib(DR_PCA,
choice = "var",
axes = 1:2) +
labs(title = "Principal Component Analysis : Descriptor Variable Contribution",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Testing the statistical significance
# of the contribution
# of the descriptor variables
# for the the Top 1 and 2 principal components
##################################
DR_PCA_VariableContributionTest <- dimdesc(DR_PCA,
axes = c(1,2),
proba = 0.05)
##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 1 principal component
##################################
(DR_PCA_PC1VariableContributors <- fviz_contrib(DR_PCA,
choice = "var",
axes = 1) +
labs(title = "Principal Component Analysis : Descriptor Variable Contribution",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Testing the statistical significance
# of the contribution
# of the descriptor variables
# for the Top 1 principal component
##################################
DR_PCA_VariableContributionTest$Dim.1##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## Tomatometer_Critic 0.7160011 4.384744e-21
## IMDB_Audience 0.7133572 7.103853e-21
## Tomatometer_Audience 0.6589988 4.925052e-17
## IMDB_Critic 0.5746051 1.986144e-12
## Nomination_SuccessRate 0.5520012 2.086140e-11
## Nominations_Total 0.3594166 3.577176e-05##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 2 principal component
##################################
(DR_PCA_PC2VariableContributors <- fviz_contrib(DR_PCA,
choice = "var",
axes = 2) +
labs(title = "Principal Component Analysis : Descriptor Variable Contribution",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Testing the statistical significance
# of the contribution
# of the descriptor variables
# for the Top 2 principal component
##################################
DR_PCA_VariableContributionTest$Dim.2##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## IMDB_Critic 0.7789894 6.683142e-27
## Tomatometer_Critic 0.6120866 2.639968e-14
## Nomination_SuccessRate -0.3771804 1.339456e-05
## Tomatometer_Audience -0.5110200 9.715208e-10
## IMDB_Audience -0.5220745 3.624252e-10##################################
# Extracting the PCA individual scores
##################################
DR_PCA_IND <- get_pca_ind(DR_PCA)
##################################
# Extracting the coordinates
# representing the scores
# for the individuals
##################################
DR_PCA_IND$coord[,c("Dim.1","Dim.2")]## Dim.1 Dim.2
## Avatar 0.267696540 -0.530442152
## The Blind Side -2.195453708 -3.301208059
## District 9 -0.430797744 0.112896306
## An Education -1.058977961 1.182366388
## The Hurt Locker 1.705555201 0.769878023
## Inglourious Basterds 0.487479202 -1.390603430
## Precious: Based on the Novel 'Push' by Sapphire -0.824912508 0.640551052
## A Serious Man -2.274858904 2.012978851
## Up 1.968871570 -0.415625889
## Up in the Air -0.948551664 0.937195852
## Black Swan -0.088494191 -0.715371246
## The Fighter 0.593337935 -0.511337506
## Inception 2.000141368 -2.400531058
## The Kids Are All Right -1.677629729 1.814279497
## The King's Speech 2.022535144 -0.140319446
## 127 Hours -0.376296841 0.640551980
## The Social Network 1.571785943 0.646156669
## Toy Story 3 2.112408569 -0.190945586
## True Grit 0.143820607 0.632433896
## Winter's Bone -1.197590702 1.942394429
## The Artist 1.829965512 0.030391009
## The Descendants -0.928054041 0.633597837
## Extremely Loud & Incredibly Close -6.607718620 -2.191543916
## The Help -0.780439361 -2.582418858
## Hugo 0.540836116 0.530503658
## Midnight in Paris -0.016386835 0.074821615
## Moneyball 0.032152643 0.821762000
## The Tree of Life -3.183193524 2.259276875
## War Horse -2.651283351 -0.011313828
## Amour 0.676678866 0.800609934
## Argo 1.295486139 -0.004493834
## Beasts of the Southern Wild -1.641594932 1.198443100
## Django Unchained 1.368398632 -1.582284768
## Les Miserables -1.786154693 -1.772901843
## Life of Pi 0.680921689 -0.635955517
## Lincoln -0.026274204 1.034913302
## Silver Linings Playbook 0.237579503 0.153926881
## Zero Dark Thirty -0.146040932 1.308036691
## American Hustle -0.743744716 1.987726848
## Captain Phillips 0.207250822 0.136428053
## Dallas Buyers Club 1.095154638 -1.098634659
## Gravity 1.808662879 0.792462032
## Her 0.707449019 0.525283745
## Nebraska -0.204598544 0.653651613
## Philomena -0.503197773 -0.094529799
## 12 Years a Slave 2.100854560 0.279285345
## The Wolf of Wall Street -0.663039400 -1.076259636
## American Sniper -1.844409883 -0.993999809
## Birdman or (The Unexpected Virtue of Ignorance) 0.621586316 0.408398188
## Boyhood 0.989609154 1.460184615
## The Grand Budapest Hotel 1.634209716 -0.286179436
## The Imitation Game 0.411500335 -1.065031194
## Selma 0.411542825 -0.068773038
## The Theory of Everything -1.003995061 -1.116933111
## Whiplash 2.611370669 -1.249717667
## The Big Short 0.170060595 -0.385300448
## Bridge of Spies 0.009676416 0.045721157
## Brooklyn -0.114157904 1.010762460
## Mad Max: Fury Road 2.337559214 -0.106023934
## The Martian 0.473734478 -0.357771031
## The Revenant 0.161937864 -1.138614186
## Room 1.196463021 -0.545134110
## Spotlight 1.989250915 -0.009168248
## Arrival 0.367309471 0.248612994
## Fences -1.186448927 0.815944510
## Hacksaw Ridge 0.404570037 -1.823823948
## Hell or High Water 0.153324144 0.884752265
## Hidden Figures -0.134558405 -0.586009309
## La La Land 1.829415815 0.497221042
## Lion -0.381467753 -1.365827706
## Manchester by the Sea 0.858671370 1.150335634
## Moonlight 0.896841919 1.777793051
## Call Me by Your Name 0.788578813 0.607403297
## Darkest Hour -0.795263816 -0.439185974
## Dunkirk 0.996564353 0.675675583
## Get Out 0.555076960 0.412865802
## Lady Bird -0.206141307 1.941822125
## Phantom Thread -0.786011564 1.540594077
## The Post -1.990318557 1.229655961
## The Shape of Water -0.018542859 1.459937812
## Three Billboards outside Ebbing, Missouri 1.118764632 -0.268033382
## Black Panther 0.279104946 1.057646892
## BlacKkKlansman 0.004769683 0.717101841
## Bohemian Rhapsody -1.483775371 -4.490215441
## The Favourite -0.331512533 1.843510513
## Green Book 0.468063042 -2.803170545
## Roma 0.714350361 1.696574201
## A Star Is Born -0.066617113 0.839660667
## Vice -3.934949029 -0.587917055
## Ford v Ferrari 1.682435065 -1.473745599
## The Irishman 0.944030071 1.164389790
## Jojo Rabbit -0.648230212 -2.470061984
## Joker -0.430208286 -3.099021343
## Little Women 1.096244053 0.365296701
## Marriage Story 0.942403658 0.774052883
## 1917 1.129721748 -1.028531120
## Once upon a Time...in Hollywood -0.741237528 0.734591165
## Parasite 3.117196230 -0.468032148
## The Father 1.929415735 -0.291670041
## Judas and the Black Messiah 0.960737989 0.162489630
## Mank -2.345763071 1.570456017
## Minari 0.422910493 1.064998675
## Nomadland 0.428470433 0.797058184
## Promising Young Woman -0.483645104 -0.425451081
## Sound of Metal 0.944143148 -0.069194279
## The Trial of the Chicago 7 -0.285898871 -0.355149365
## Belfast -0.511582058 -0.429370787
## CODA 1.758254848 -2.156598920
## Don't Look Up -4.442451275 -2.539922441
## Drive My Car 0.158306636 1.192487916
## Dune 1.122203185 -1.826980124
## King Richard 0.257879939 -0.723422523
## Licorice Pizza -1.872711748 2.147715796
## Nightmare Alley -3.160384027 0.636761057
## The Power of the Dog -0.720311839 2.283065628
## West Side Story 0.044190625 0.446398144
## All Quiet on the Western Front 0.952314310 -0.952191110
## Avatar: The Way of Water -0.923072631 -2.037690509
## The Banshees of Inisherin -0.069099854 1.439223633
## Elvis -1.434462767 -1.387741046
## Everything Everywhere All at Once 1.594787307 -0.536995405
## The Fabelmans -0.253962254 0.721795892
## Tar -0.777644395 1.584983545
## Top Gun: Maverick 1.673321316 -1.169382857
## Triangle of Sadness -3.612891352 -0.558900276
## Women Talking -1.120884714 0.372860732##################################
# Extracting the quality of representation
# for the individuals
# on the factor map
##################################
DR_PCA_IND$cos2[,c("Dim.1","Dim.2")]## Dim.1 Dim.2
## Avatar 3.473559e-02 1.363846e-01
## The Blind Side 2.654492e-01 6.001760e-01
## District 9 7.241199e-02 4.973054e-03
## An Education 2.532809e-01 3.157423e-01
## The Hurt Locker 3.809304e-01 7.761718e-02
## Inglourious Basterds 4.920414e-02 4.004019e-01
## Precious: Based on the Novel 'Push' by Sapphire 2.482848e-01 1.497069e-01
## A Serious Man 4.651816e-01 3.642437e-01
## Up 7.139238e-01 3.181429e-02
## Up in the Air 4.213049e-01 4.112778e-01
## Black Swan 5.990845e-03 3.914908e-01
## The Fighter 4.524012e-01 3.359966e-01
## Inception 3.476223e-01 5.007269e-01
## The Kids Are All Right 4.166793e-01 4.873243e-01
## The King's Speech 5.886048e-01 2.833136e-03
## 127 Hours 8.087118e-02 2.343373e-01
## The Social Network 7.817410e-01 1.321149e-01
## Toy Story 3 7.432579e-01 6.072995e-03
## True Grit 5.845162e-03 1.130276e-01
## Winter's Bone 2.367355e-01 6.227610e-01
## The Artist 7.071045e-01 1.950240e-04
## The Descendants 5.169605e-01 2.409563e-01
## Extremely Loud & Incredibly Close 8.695189e-01 9.564809e-02
## The Help 7.634343e-02 8.358854e-01
## Hugo 6.084654e-02 5.854385e-02
## Midnight in Paris 2.416386e-04 5.037676e-03
## Moneyball 5.166937e-04 3.375141e-01
## The Tree of Life 6.076654e-01 3.061099e-01
## War Horse 9.579033e-01 1.744329e-05
## Amour 1.885396e-01 2.639242e-01
## Argo 7.313005e-01 8.799629e-06
## Beasts of the Southern Wild 5.654711e-01 3.013792e-01
## Django Unchained 3.393579e-01 4.537347e-01
## Les Miserables 3.367003e-01 3.317223e-01
## Life of Pi 1.238295e-01 1.080148e-01
## Lincoln 1.224060e-04 1.899116e-01
## Silver Linings Playbook 6.949945e-02 2.917376e-02
## Zero Dark Thirty 8.195024e-03 6.574169e-01
## American Hustle 8.482517e-02 6.058853e-01
## Captain Phillips 2.053377e-02 8.897817e-03
## Dallas Buyers Club 3.810563e-01 3.834818e-01
## Gravity 3.507612e-01 6.733692e-02
## Her 2.375703e-01 1.309754e-01
## Nebraska 2.728446e-02 2.784857e-01
## Philomena 8.576662e-02 3.026762e-03
## 12 Years a Slave 8.635690e-01 1.526164e-02
## The Wolf of Wall Street 9.216683e-02 2.428455e-01
## American Sniper 6.302903e-01 1.830620e-01
## Birdman or (The Unexpected Virtue of Ignorance) 1.480236e-01 6.389924e-02
## Boyhood 2.276680e-01 4.956671e-01
## The Grand Budapest Hotel 7.454044e-01 2.285879e-02
## The Imitation Game 5.353337e-02 3.585988e-01
## Selma 2.783596e-02 7.773426e-04
## The Theory of Everything 4.276720e-01 5.293001e-01
## Whiplash 6.665594e-01 1.526601e-01
## The Big Short 3.656899e-02 1.877174e-01
## Bridge of Spies 2.143375e-04 4.785238e-03
## Brooklyn 2.858225e-03 2.240695e-01
## Mad Max: Fury Road 7.394092e-01 1.521134e-03
## The Martian 7.606632e-02 4.338431e-02
## The Revenant 3.895087e-03 1.925633e-01
## Room 3.736193e-01 7.755994e-02
## Spotlight 8.440420e-01 1.792907e-05
## Arrival 1.082896e-01 4.961011e-02
## Fences 3.887748e-01 1.838744e-01
## Hacksaw Ridge 4.540692e-02 9.227848e-01
## Hell or High Water 6.426268e-03 2.139839e-01
## Hidden Figures 3.432981e-03 6.511166e-02
## La La Land 3.054422e-01 2.256333e-02
## Lion 3.165926e-02 4.058607e-01
## Manchester by the Sea 2.344310e-01 4.207366e-01
## Moonlight 1.580445e-01 6.210264e-01
## Call Me by Your Name 2.288301e-01 1.357617e-01
## Darkest Hour 4.279259e-01 1.305098e-01
## Dunkirk 4.223402e-01 1.941459e-01
## Get Out 1.483425e-01 8.206861e-02
## Lady Bird 9.052534e-03 8.032653e-01
## Phantom Thread 1.701626e-01 6.537063e-01
## The Post 5.387903e-01 2.056562e-01
## The Shape of Water 3.675095e-05 2.278158e-01
## Three Billboards outside Ebbing, Missouri 6.958869e-01 3.994284e-02
## Black Panther 2.586023e-02 3.713459e-01
## BlacKkKlansman 2.405407e-05 5.437147e-01
## Bohemian Rhapsody 8.015624e-02 7.340665e-01
## The Favourite 1.822222e-02 5.634984e-01
## Green Book 2.383626e-02 8.549259e-01
## Roma 8.290181e-02 4.676136e-01
## A Star Is Born 3.819042e-03 6.067229e-01
## Vice 7.328548e-01 1.635957e-02
## Ford v Ferrari 4.016954e-01 3.082231e-01
## The Irishman 1.801827e-01 2.741184e-01
## Jojo Rabbit 5.215222e-02 7.572338e-01
## Joker 1.159945e-02 6.019064e-01
## Little Women 4.704613e-01 5.223972e-02
## Marriage Story 3.958672e-01 2.670649e-01
## 1917 3.152575e-01 2.613108e-01
## Once upon a Time...in Hollywood 1.155997e-01 1.135360e-01
## Parasite 7.896317e-01 1.780113e-02
## The Father 8.341746e-01 1.906290e-02
## Judas and the Black Messiah 2.520046e-01 7.208583e-03
## Mank 4.052969e-01 1.816588e-01
## Minari 7.906691e-02 5.014135e-01
## Nomadland 5.220968e-02 1.806714e-01
## Promising Young Woman 1.636160e-01 1.266110e-01
## Sound of Metal 5.282852e-01 2.837482e-03
## The Trial of the Chicago 7 3.585289e-02 5.532499e-02
## Belfast 9.399917e-02 6.621531e-02
## CODA 1.728471e-01 2.600382e-01
## Don't Look Up 7.434192e-01 2.430129e-01
## Drive My Car 8.639278e-03 4.902157e-01
## Dune 1.778672e-01 4.714335e-01
## King Richard 1.700203e-02 1.337980e-01
## Licorice Pizza 3.582575e-01 4.712019e-01
## Nightmare Alley 9.299245e-01 3.775035e-02
## The Power of the Dog 4.566770e-02 4.587803e-01
## West Side Story 6.014453e-04 6.137346e-02
## All Quiet on the Western Front 3.088681e-01 3.087882e-01
## Avatar: The Way of Water 1.423211e-01 6.935438e-01
## The Banshees of Inisherin 1.175231e-03 5.098300e-01
## Elvis 2.363814e-01 2.212339e-01
## Everything Everywhere All at Once 3.661492e-01 4.151392e-02
## The Fabelmans 4.282869e-02 3.459595e-01
## Tar 1.591355e-01 6.610807e-01
## Top Gun: Maverick 3.950945e-01 1.929549e-01
## Triangle of Sadness 9.230537e-01 2.208950e-02
## Women Talking 1.450523e-01 1.605077e-02##################################
# Extracting the contributions
# (in percentage) of the individuals
# to the principal components
##################################
DR_PCA_IND$contrib[,c("Dim.1","Dim.2")]## Dim.1 Dim.2
## Avatar 2.562046e-02 1.341083e-01
## The Blind Side 1.723257e+00 5.194282e+00
## District 9 6.635113e-02 6.074901e-03
## An Education 4.009363e-01 6.663216e-01
## The Hurt Locker 1.039999e+00 2.825033e-01
## Inglourious Basterds 8.495984e-02 9.216930e-01
## Precious: Based on the Novel 'Push' by Sapphire 2.432861e-01 1.955632e-01
## A Serious Man 1.850165e+00 1.931337e+00
## Up 1.385914e+00 8.233508e-02
## Up in the Air 3.216796e-01 4.186397e-01
## Black Swan 2.799826e-03 2.439173e-01
## The Fighter 1.258652e-01 1.246221e-01
## Inception 1.430286e+00 2.746593e+00
## The Kids Are All Right 1.006222e+00 1.568874e+00
## The King's Speech 1.462492e+00 9.384593e-03
## 127 Hours 5.062472e-02 1.955638e-01
## The Social Network 8.832594e-01 1.990011e-01
## Toy Story 3 1.595355e+00 1.737797e-02
## True Grit 7.395094e-03 1.906382e-01
## Winter's Bone 5.127649e-01 1.798269e+00
## The Artist 1.197257e+00 4.402202e-04
## The Descendants 3.079272e-01 1.913406e-01
## Extremely Loud & Incredibly Close 1.561006e+01 2.289181e+00
## The Help 2.177609e-01 3.178580e+00
## Hugo 1.045762e-01 1.341394e-01
## Midnight in Paris 9.600452e-05 2.668295e-03
## Moneyball 3.696024e-04 3.218636e-01
## The Tree of Life 3.622660e+00 2.432868e+00
## War Horse 2.513123e+00 6.100969e-05
## Amour 1.637068e-01 3.055073e-01
## Argo 6.000218e-01 9.625289e-06
## Beasts of the Southern Wild 9.634596e-01 6.845648e-01
## Django Unchained 6.694633e-01 1.193298e+00
## Les Miserables 1.140616e+00 1.498129e+00
## Life of Pi 1.657661e-01 1.927672e-01
## Lincoln 2.468088e-04 5.104905e-01
## Silver Linings Playbook 2.017992e-02 1.129298e-02
## Zero Dark Thirty 7.625190e-03 8.154917e-01
## American Hustle 1.977649e-01 1.883186e+00
## Captain Phillips 1.535656e-02 8.871296e-03
## Dallas Buyers Club 4.287976e-01 5.752893e-01
## Gravity 1.169544e+00 2.993206e-01
## Her 1.789336e-01 1.315127e-01
## Nebraska 1.496603e-02 2.036444e-01
## Philomena 9.052716e-02 4.259094e-03
## 12 Years a Slave 1.577951e+00 3.717714e-02
## The Wolf of Wall Street 1.571738e-01 5.520950e-01
## American Sniper 1.216232e+00 4.709256e-01
## Birdman or (The Unexpected Virtue of Ignorance) 1.381352e-01 7.949638e-02
## Boyhood 3.501297e-01 1.016238e+00
## The Grand Budapest Hotel 9.548102e-01 3.903521e-02
## The Imitation Game 6.053992e-02 5.406353e-01
## Selma 6.055243e-02 2.254323e-03
## The Theory of Everything 3.603833e-01 5.946125e-01
## Whiplash 2.438027e+00 7.443951e-01
## The Big Short 1.033972e-02 7.075852e-02
## Bridge of Spies 3.347577e-05 9.963551e-04
## Brooklyn 4.659223e-03 4.869428e-01
## Mad Max: Fury Road 1.953560e+00 5.357813e-03
## The Martian 8.023641e-02 6.100846e-02
## The Revenant 9.375583e-03 6.179209e-01
## Room 5.117997e-01 1.416402e-01
## Spotlight 1.414753e+00 4.006383e-05
## Arrival 4.823538e-02 2.945963e-02
## Fences 5.032683e-01 3.173226e-01
## Hacksaw Ridge 5.851792e-02 1.585424e+00
## Hell or High Water 8.404707e-03 3.730981e-01
## Hidden Figures 6.473261e-03 1.636774e-01
## La La Land 1.196538e+00 1.178362e-01
## Lion 5.202561e-02 8.891429e-01
## Manchester by the Sea 2.636061e-01 6.307088e-01
## Moonlight 2.875632e-01 1.506406e+00
## Call Me by Your Name 2.223267e-01 1.758466e-01
## Darkest Hour 2.261122e-01 9.193410e-02
## Dunkirk 3.550685e-01 2.175986e-01
## Get Out 1.101559e-01 8.124517e-02
## Lady Bird 1.519258e-02 1.797209e+00
## Phantom Thread 2.208815e-01 1.131244e+00
## The Post 1.416272e+00 7.206874e-01
## The Shape of Water 1.229291e-04 1.015894e+00
## Three Billboards outside Ebbing, Missouri 4.474855e-01 3.424187e-02
## Black Panther 2.785073e-02 5.331644e-01
## BlacKkKlansman 8.133558e-06 2.450989e-01
## Bohemian Rhapsody 7.871143e-01 9.609794e+00
## The Favourite 3.929175e-02 1.619836e+00
## Green Book 7.832676e-02 3.745232e+00
## Roma 1.824417e-01 1.371909e+00
## A Star Is Born 1.586621e-03 3.360372e-01
## Vice 5.535791e+00 1.647448e-01
## Ford v Ferrari 1.011994e+00 1.035201e+00
## The Irishman 3.186201e-01 6.462142e-01
## Jojo Rabbit 1.502312e-01 2.908007e+00
## Joker 6.616968e-02 4.577505e+00
## Little Women 4.296512e-01 6.360206e-02
## Marriage Story 3.175232e-01 2.855755e-01
## 1917 4.562937e-01 5.042136e-01
## Once upon a Time...in Hollywood 1.964338e-01 2.572001e-01
## Parasite 3.474000e+00 1.044074e-01
## The Father 1.330924e+00 4.054743e-02
## Judas and the Black Messiah 3.299981e-01 1.258436e-02
## Mank 1.967296e+00 1.175523e+00
## Minari 6.394379e-02 5.406022e-01
## Nomadland 6.563617e-02 3.028027e-01
## Promising Young Woman 8.362865e-02 8.627381e-02
## Sound of Metal 3.186964e-01 2.282023e-03
## The Trial of the Chicago 7 2.922311e-02 6.011762e-02
## Belfast 9.356902e-02 8.787082e-02
## CODA 1.105262e+00 2.216759e+00
## Don't Look Up 7.055809e+00 3.074827e+00
## Drive My Car 8.959829e-03 6.777783e-01
## Dune 4.502404e-01 1.590916e+00
## King Richard 2.377588e-02 2.494387e-01
## Licorice Pizza 1.253844e+00 2.198535e+00
## Nightmare Alley 3.570929e+00 1.932559e-01
## The Power of the Dog 1.854994e-01 2.484371e+00
## West Side Story 6.981710e-04 9.497832e-02
## All Quiet on the Western Front 3.242367e-01 4.321435e-01
## Avatar: The Way of Water 3.046304e-01 1.979047e+00
## The Banshees of Inisherin 1.707087e-03 9.872708e-01
## Elvis 7.356649e-01 9.179026e-01
## Everything Everywhere All at Once 9.092997e-01 1.374424e-01
## The Fabelmans 2.305897e-02 2.483182e-01
## Tar 2.162039e-01 1.197372e+00
## Top Gun: Maverick 1.001060e+00 6.517682e-01
## Triangle of Sadness 4.666715e+00 1.488841e-01
## Women Talking 4.491831e-01 6.626329e-02##################################
# Extracting the correlation
# between the individual instances
# grouped by Picture categories
# and top principal components
##################################
(DR_PCA_IndividualCorrelationCircleByPicture <- fviz_pca_ind(DR_PCA,
geom.ind = "text",
col.ind = SD_PCA$Picture,
palette = c("#888888","#5544FF"),
repel = TRUE,
legend.title = "Picture",
addEllipses = FALSE) +
labs(title = "Principal Component Analysis : Factorial Map of Individuals",
subtitle = "Principal Components Versus Individuals Grouped by Picture Categories",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Extracting the correlation
# between the individual instances
# grouped by Year categories
# and top principal components
##################################
(DR_PCA_IndividualCorrelationCircleByYear <- fviz_pca_ind(DR_PCA,
geom.ind = "text",
col.ind = SD_PCA$Year,
repel = TRUE,
legend.title = "Year",
addEllipses = FALSE) +
labs(title = "Principal Component Analysis : Factorial Map of Individuals",
subtitle = "Principal Components Versus Individuals Grouped by Picture Categories",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 1 and Top 2 principal components
##################################
(DR_PCA_PCIndividualContributors <- fviz_contrib(DR_PCA,
choice = "ind",
axes = 1:2,
top = 10) +
labs(title = "Principal Component Analysis : Individual Contribution",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 1 principal component
##################################
(DR_PCA_PC1IndividualContributors <- fviz_contrib(DR_PCA,
choice = "ind",
axes = 1,
top = 10) +
labs(title = "Principal Component Analysis : Individual Contribution",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 2 principal component
##################################
(DR_PCA_PC2IndividualContributors <- fviz_contrib(DR_PCA,
choice = "ind",
axes = 2,
top = 10) +
labs(title = "Principal Component Analysis : Individual Contribution",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Formulating the Biplot
# using the individual scores
# and descriptor variable loadings
# for the Top 1 and Top 2 principal components
##################################
(DR_PCA_Biplot <- fviz_pca_biplot(DR_PCA,
label = c("var","ind"),
repel = TRUE,
habillage = SD_PCA$Picture,
palette = c("#888888","#5544FF"),
col.var = "#FF5050",
legend.title = "Picture",
addEllipses = FALSE) +
labs(title = "Principal Component Analysis : Biplot",
subtitle = "Individual Scores versus Descriptor Variable Loadings",
x = "Principal Component 1",
y = "Principal Component 2") +
theme_classic() +
theme(legend.position="top"))
1.5.2 Correspondence Analysis (CA)
Correspondence Analysis employs a statistical method for summarizing tables and analyzing the relationship between two or more categorical variables. It is a data visualization technique that aims to find patterns and associations between the categories of different variables. A contingency table is created to represent the frequencies or counts of the categories of the variables. The contingency table is then transformed into a matrix of proportions or percentages to normalize the data by computing row and column averages, expected values and residuals. The method then calculates the principal components of the normalized matrix and maps the variables and categories onto a two-dimensional plot based on their proximity to each other. The plot displays the patterns and associations between the variables and categories, with closer proximity indicating a stronger relationship.
[A] Evaluating both Cinematography and Genre descriptors, Cinematography=WON was observed to be associated with Genre=Sci-Fi and Genre=Adventure. These included Sci-Fi movies like Avatar, Inception, Gravity and Dune; and adventure movies like Life of Pi and Hugo.
[B] Evaluating both Directing and Genre descriptors, Directing=WON was observed to be associated with Genre=Western and Genre=Musical. These included Western movies like The Revenant and The Power of the Dog; and musical movies like La La Land.
[C] Evaluating both Editing and Genre descriptors, Editing=WON was observed to be associated with Genre=War and Genre=Music. These included war movies like The Hurt Locker, Hacksaw Ridge and Dunkirk; and music movies like Whiplash and The Sound of Metal.
[D] Evaluating both Screenplay and Genre descriptors, Screenplay=WON was observed to be associated with Genre=LGBTQ+, Genre=Thriller and Genre=Comedy. These included LGBTQ+ movies like Moonlight and Call me By Your Name; thriller movies like Get Out, Parasite and Promising Young Woman; and comedy movies like The Descendants, Her, Birdman or (The Unexpected Virtue of Ignorance), The Big Short, BlacKkKlansman, Green Book, Jojo Rabbit and Everything Everywhere All at Once.
##################################
# Loading dataset for Cinematography
##################################
SD_CA_Cinematography <- Oscars.CA.Cinematography
str(SD_CA_Cinematography)## 'data.frame': 16 obs. of 3 variables:
## $ NNOM: int 3 1 8 17 3 22 2 8 2 2 ...
## $ NOM : int 1 0 3 4 2 2 0 6 1 1 ...
## $ WON : int 0 2 1 1 0 1 0 0 0 0 ...balloonplot(t(as.table(as.matrix(SD_CA_Cinematography))),
main="Cinematography by Film Genre",
xlab="Cinematography",
ylab="Genre",
label=FALSE,
show.margins=FALSE)
##################################
# Conducting a Chi-Square Test
##################################
(SD_CA_Cinematography_CHSQ <- chisq.test(SD_CA_Cinematography))##
## Pearson's Chi-squared test
##
## data: SD_CA_Cinematography
## X-squared = 53.85, df = 30, p-value = 0.004777##################################
# Performing CA
##################################
DR_CA_Cinematography <- CA(SD_CA_Cinematography,
graph = FALSE)
##################################
# Obtaining the CA eigenvalues
##################################
(DR_CA_Cinematography_EV <- get_eigenvalue(DR_CA_Cinematography))## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 0.2992796 70.02615 70.02615
## Dim.2 0.1281030 29.97385 100.00000##################################
# Formulating the Scree Plot
# for the variances
##################################
(DR_CA_Cinematography_VarianceScreePlot <- fviz_eig(DR_CA_Cinematography,
addlabels = TRUE,
ylim = c(0, 100),
choice = c("variance")) +
labs(title = "Correspondence Analysis : Scree Plot of Explained Variances (Cinematography)",
subtitle = "Top 2 Principal Components",
y = "Percentage of Explained Variances",
x = "Principal Components") +
theme_classic())
##################################
# Formulating the Scree Plot
# for the eigenvalues
##################################
(DR_CA_Cinematography_EigenvalueScreePlot <- fviz_eig(DR_CA_Cinematography,
addlabels = TRUE,
ylim = c(0, 6),
choice = c("eigenvalue")) +
labs(title = "Correspondence Analysis : Scree Plot of Eigenvalues (Cinematography)",
subtitle = "Top 2 Principal Components",
y = "Eigenvalues",
x = "Principal Components") +
theme_classic())
##################################
# Extracting the CA
# results for row descriptor variables
##################################
(DR_CA_Cinematography_ROW <- get_ca_row(DR_CA_Cinematography))## Correspondence Analysis - Results for rows
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the rows"
## 2 "$cos2" "Cos2 for the rows"
## 3 "$contrib" "contributions of the rows"
## 4 "$inertia" "Inertia of the rows"##################################
# Extracting the coordinates
# representing the loadings
# for the row descriptor variabless
##################################
DR_CA_Cinematography_ROW$coord## Dim 1 Dim 2
## Action -0.35048211 0.041667147
## Adventure 1.61952041 -0.927278781
## Biography -0.07606662 -0.012566854
## Comedy -0.26225224 -0.133844287
## Crime -0.21528924 0.362711502
## Drama -0.37198127 -0.348215442
## Family -0.57580357 -0.493406778
## History -0.18953822 0.423862808
## LGBTQ+ -0.27537496 0.220025122
## Music -0.27537496 0.220025122
## Musical 0.82228703 0.003089121
## Romance -0.21528924 0.362711502
## Sci-Fi 1.08803149 -0.307033513
## Thriller -0.27537496 0.220025122
## War 0.97250133 0.359805071
## Western 0.92340729 0.949112996##################################
# Extracting the quality of representation
# for the row descriptor variables
# on the factor map
##################################
DR_CA_Cinematography_ROW$cos2## Dim 1 Dim 2
## Action 0.9860633 1.393672e-02
## Adventure 0.7531088 2.468912e-01
## Biography 0.9734313 2.656869e-02
## Comedy 0.7933535 2.066465e-01
## Crime 0.2605233 7.394767e-01
## Drama 0.5329632 4.670368e-01
## Family 0.5766083 4.233917e-01
## History 0.1666388 8.333612e-01
## LGBTQ+ 0.6103501 3.896499e-01
## Music 0.6103501 3.896499e-01
## Musical 0.9999859 1.411291e-05
## Romance 0.2605233 7.394767e-01
## Sci-Fi 0.9262414 7.375862e-02
## Thriller 0.6103501 3.896499e-01
## War 0.8795969 1.204031e-01
## Western 0.4862747 5.137253e-01##################################
# Extracting the contributions
# (in percentage) of the row descriptor variables
# to the principal components
##################################
DR_CA_Cinematography_ROW$contrib## Dim 1 Dim 2
## Action 1.3029990 4.302467e-02
## Adventure 20.8663496 1.598129e+01
## Biography 0.1841288 1.174098e-02
## Comedy 4.0124854 2.441701e+00
## Crime 0.6145639 4.075329e+00
## Drama 9.1734884 1.878046e+01
## Family 1.7584543 3.016548e+00
## History 1.3337486 1.558292e+01
## LGBTQ+ 0.6032850 8.997790e-01
## Music 0.6032850 8.997790e-01
## Musical 5.3792349 1.773622e-04
## Romance 0.6145639 4.075329e+00
## Sci-Fi 28.2538615 5.256348e+00
## Thriller 1.2065700 1.799558e+00
## War 15.0481819 4.812335e+00
## Western 9.0447999 2.232369e+01##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 1 and 2 principal components
##################################
(DR_CA_Cinematography_ROW_PCVariableContributors <- fviz_contrib(DR_CA_Cinematography,
choice = "row",
axes = 1:2) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Cinematography)",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 1 principal component
##################################
(DR_CA_Cinematography_ROW_PC1VariableContributors <- fviz_contrib(DR_CA_Cinematography,
choice = "row",
axes = 1) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Cinematography)",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 2 principal component
##################################
(DR_CA_Cinematography_ROW_PC2VariableContributors <- fviz_contrib(DR_CA_Cinematography,
choice = "row",
axes = 2) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Cinematography)",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the CA
# results for column descriptor variables
##################################
(DR_CA_Cinematography_COL <- get_ca_col(DR_CA_Cinematography))## Correspondence Analysis - Results for columns
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the columns"
## 2 "$cos2" "Cos2 for the columns"
## 3 "$contrib" "contributions of the columns"
## 4 "$inertia" "Inertia of the columns"##################################
# Extracting the coordinates
# representing the loadings
# for the column descriptor variabless
##################################
DR_CA_Cinematography_COL$coord## Dim 1 Dim 2
## NNOM -0.3150017 -0.1765976
## NOM 0.1780598 0.5894460
## WON 1.4864741 -0.4095314##################################
# Extracting the quality of representation
# for the column descriptor variables
# on the factor map
##################################
DR_CA_Cinematography_COL$cos2## Dim 1 Dim 2
## NNOM 0.76086152 0.23913848
## NOM 0.08362161 0.91637839
## WON 0.92945168 0.07054832##################################
# Extracting the contributions
# (in percentage) of the column descriptor variables
# to the principal components
##################################
DR_CA_Cinematography_COL$contrib## Dim 1 Dim 2
## NNOM 21.050778 15.45716
## NOM 2.774585 71.03494
## WON 76.174637 13.50790##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 1 and 2 principal components
##################################
(DR_CA_Cinematography_COL_PCVariableContributors <- fviz_contrib(DR_CA_Cinematography,
choice = "col",
axes = 1:2) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Cinematography)",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 1 principal component
##################################
(DR_CA_Cinematography_COL_PC1VariableContributors <- fviz_contrib(DR_CA_Cinematography,
choice = "col",
axes = 1) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Cinematography)",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 2 principal component
##################################
(DR_CA_Cinematography_COL_PC2VariableContributors <- fviz_contrib(DR_CA_Cinematography,
choice = "col",
axes = 2) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Cinematography)",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Formulating the Symmetric Biplot
# using the row and column
# descriptor variable loadings
# for the Top 1 and Top 2 principal components
##################################
(DR_CA_SymmetricBiplot <- fviz_ca_biplot(DR_CA_Cinematography,
label="all",
geom = "text",
repel = TRUE) +
labs(title = "Correspondence Analysis : Symmetric Biplot (Cinematography)",
subtitle = "Row versus Column Descriptor Variable Loadings",
x = "Principal Component 1",
y = "Principal Component 2") +
theme_classic())
##################################
# Formulating the Asymmetric Biplot
# using the row and column
# descriptor variable loadings
# for the Top 1 and Top 2 principal components
##################################
(DR_CA_SymmetricBiplot <- fviz_ca_biplot(DR_CA_Cinematography,
label="all",
geom = "text",
repel = TRUE,
map = "symbiplot") +
labs(title = "Correspondence Analysis : Asymmetric Biplot (Cinematography)",
subtitle = "Row versus Column Descriptor Variable Loadings",
x = "Principal Component 1",
y = "Principal Component 2") +
theme_classic())
##################################
# Loading dataset for Directing
##################################
SD_CA_Directing <- Oscars.CA.Directing
str(SD_CA_Directing)## 'data.frame': 16 obs. of 3 variables:
## $ NNOM: int 3 0 8 6 2 12 2 10 2 2 ...
## $ NOM : int 1 2 4 14 3 11 0 3 1 1 ...
## $ WON : int 0 1 0 2 0 2 0 1 0 0 ...balloonplot(t(as.table(as.matrix(SD_CA_Directing))),
main="Directing by Film Genre",
xlab="Directing",
ylab="Genre",
label=FALSE,
show.margins=FALSE)
##################################
# Conducting a Chi-Square Test
##################################
(SD_CA_Directing_CHSQ <- chisq.test(SD_CA_Directing))##
## Pearson's Chi-squared test
##
## data: SD_CA_Directing
## X-squared = 32.369, df = 30, p-value = 0.3506##################################
# Performing CA
##################################
DR_CA_Directing <- CA(SD_CA_Directing,
graph = FALSE)
##################################
# Obtaining the CA eigenvalues
##################################
(DR_CA_Directing_EV <- get_eigenvalue(DR_CA_Directing))## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 0.16679328 64.92707 64.92707
## Dim.2 0.09009999 35.07293 100.00000##################################
# Formulating the Scree Plot
# for the variances
##################################
(DR_CA_Directing_VarianceScreePlot <- fviz_eig(DR_CA_Directing,
addlabels = TRUE,
ylim = c(0, 100),
choice = c("variance")) +
labs(title = "Correspondence Analysis : Scree Plot of Explained Variances (Directing)",
subtitle = "Top 2 Principal Components",
y = "Percentage of Explained Variances",
x = "Principal Components") +
theme_classic())
##################################
# Formulating the Scree Plot
# for the eigenvalues
##################################
(DR_CA_Directing_EigenvalueScreePlot <- fviz_eig(DR_CA_Directing,
addlabels = TRUE,
ylim = c(0, 6),
choice = c("eigenvalue")) +
labs(title = "Correspondence Analysis : Scree Plot of Eigenvalues (Directing)",
subtitle = "Top 2 Principal Components",
y = "Eigenvalues",
x = "Principal Components") +
theme_classic())
##################################
# Extracting the CA
# results for row descriptor variables
##################################
(DR_CA_Directing_ROW <- get_ca_row(DR_CA_Directing))## Correspondence Analysis - Results for rows
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the rows"
## 2 "$cos2" "Cos2 for the rows"
## 3 "$contrib" "contributions of the rows"
## 4 "$inertia" "Inertia of the rows"##################################
# Extracting the coordinates
# representing the loadings
# for the row descriptor variabless
##################################
DR_CA_Directing_ROW$coord## Dim 1 Dim 2
## Action -0.59093674 0.025492372
## Adventure 1.02503716 0.076828292
## Biography -0.45370496 -0.086344034
## Comedy 0.29890560 -0.326516979
## Crime -0.01456328 -0.444220534
## Drama -0.05489268 -0.082970326
## Family -1.00263207 0.361001590
## History -0.45050428 0.204247535
## LGBTQ+ -0.45370496 -0.086344034
## Music -0.45370496 -0.086344034
## Musical 0.47611005 0.524173917
## Romance 0.21396947 0.190497611
## Sci-Fi -0.01680399 0.469783141
## Thriller 0.28566610 -0.004757871
## War 0.56012965 -0.228430683
## Western 0.80378579 0.941269298##################################
# Extracting the quality of representation
# for the row descriptor variables
# on the factor map
##################################
DR_CA_Directing_ROW$cos2## Dim 1 Dim 2
## Action 0.998142490 0.001857510
## Adventure 0.994413624 0.005586376
## Biography 0.965048427 0.034951573
## Comedy 0.455937517 0.544062483
## Crime 0.001073629 0.998926371
## Drama 0.304447910 0.695552090
## Family 0.885238705 0.114761295
## History 0.829497458 0.170502542
## LGBTQ+ 0.965048427 0.034951573
## Music 0.965048427 0.034951573
## Musical 0.452060467 0.547939533
## Romance 0.557836791 0.442163209
## Sci-Fi 0.001277834 0.998722166
## Thriller 0.999722676 0.000277324
## War 0.857401211 0.142598789
## Western 0.421701375 0.578298625##################################
# Extracting the contributions
# (in percentage) of the row descriptor variables
# to the principal components
##################################
DR_CA_Directing_ROW$contrib## Dim 1 Dim 2
## Action 6.646498031 0.022897349
## Adventure 14.998622769 0.155979791
## Biography 11.753824740 0.788044317
## Comedy 9.352800609 20.660410302
## Crime 0.005045905 8.691044740
## Drama 0.358442786 1.515969009
## Family 9.566742526 2.295899889
## History 13.520003083 5.144538317
## LGBTQ+ 2.938456185 0.197011079
## Music 2.938456185 0.197011079
## Musical 3.235838706 7.260671511
## Romance 1.089242375 1.598283421
## Sci-Fi 0.012092556 17.496133580
## Thriller 2.329804971 0.001196414
## War 8.957344701 2.757813226
## Western 12.296783873 31.217095975##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 1 and 2 principal components
##################################
(DR_CA_Directing_ROW_PCVariableContributors <- fviz_contrib(DR_CA_Directing,
choice = "row",
axes = 1:2) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Directing)",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 1 principal component
##################################
(DR_CA_Directing_ROW_PC1VariableContributors <- fviz_contrib(DR_CA_Directing,
choice = "row",
axes = 1) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Directing)",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 2 principal component
##################################
(DR_CA_Directing_ROW_PC2VariableContributors <- fviz_contrib(DR_CA_Directing,
choice = "row",
axes = 2) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Directing)",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the CA
# results for column descriptor variables
##################################
(DR_CA_Directing_COL <- get_ca_col(DR_CA_Directing))## Correspondence Analysis - Results for columns
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the columns"
## 2 "$cos2" "Cos2 for the columns"
## 3 "$contrib" "contributions of the columns"
## 4 "$inertia" "Inertia of the columns"##################################
# Extracting the coordinates
# representing the loadings
# for the column descriptor variabless
##################################
DR_CA_Directing_COL$coord## Dim 1 Dim 2
## NNOM -0.4094783 0.1083606
## NOM 0.2630727 -0.2944740
## WON 0.7297404 0.6581319##################################
# Extracting the quality of representation
# for the column descriptor variables
# on the factor map
##################################
DR_CA_Directing_COL$cos2## Dim 1 Dim 2
## NNOM 0.9345536 0.06544635
## NOM 0.4438576 0.55614244
## WON 0.5514589 0.44854113##################################
# Extracting the contributions
# (in percentage) of the column descriptor variables
# to the principal components
##################################
DR_CA_Directing_COL$contrib## Dim 1 Dim 2
## NNOM 47.07222 6.102386
## NOM 17.45333 40.483176
## WON 35.47445 53.414437##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 1 and 2 principal components
##################################
(DR_CA_Directing_COL_PCVariableContributors <- fviz_contrib(DR_CA_Directing,
choice = "col",
axes = 1:2) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Directing)",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 1 principal component
##################################
(DR_CA_Directing_COL_PC1VariableContributors <- fviz_contrib(DR_CA_Directing,
choice = "col",
axes = 1) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Directing)",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 2 principal component
##################################
(DR_CA_Directing_COL_PC2VariableContributors <- fviz_contrib(DR_CA_Directing,
choice = "col",
axes = 2) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Directing)",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Formulating the Symmetric Biplot
# using the row and column
# descriptor variable loadings
# for the Top 1 and Top 2 principal components
##################################
(DR_CA_SymmetricBiplot <- fviz_ca_biplot(DR_CA_Directing,
label="all",
geom = "text",
repel = TRUE) +
labs(title = "Correspondence Analysis : Symmetric Biplot (Directing)",
subtitle = "Row versus Column Descriptor Variable Loadings",
x = "Principal Component 1",
y = "Principal Component 2") +
theme_classic())
##################################
# Formulating the Asymmetric Biplot
# using the row and column
# descriptor variable loadings
# for the Top 1 and Top 2 principal components
##################################
(DR_CA_SymmetricBiplot <- fviz_ca_biplot(DR_CA_Directing,
label="all",
geom = "text",
repel = TRUE,
map = "symbiplot") +
labs(title = "Correspondence Analysis : Asymmetric Biplot (Directing)",
subtitle = "Row versus Column Descriptor Variable Loadings",
x = "Principal Component 1",
y = "Principal Component 2") +
theme_classic())
##################################
# Loading dataset for Editing
##################################
SD_CA_Editing <- Oscars.CA.Editing
str(SD_CA_Editing)## 'data.frame': 16 obs. of 3 variables:
## $ NNOM: int 1 1 4 11 0 19 2 7 1 0 ...
## $ NOM : int 2 2 6 10 5 6 0 5 2 1 ...
## $ WON : int 1 0 2 1 0 0 0 2 0 2 ...balloonplot(t(as.table(as.matrix(SD_CA_Editing))),
main="Editing by Film Genre",
xlab="Editing",
ylab="Genre",
label=FALSE,
show.margins=FALSE)
##################################
# Conducting a Chi-Square Test
##################################
(SD_CA_Editing_CHSQ <- chisq.test(SD_CA_Editing))##
## Pearson's Chi-squared test
##
## data: SD_CA_Editing
## X-squared = 50.873, df = 30, p-value = 0.01005##################################
# Performing CA
##################################
DR_CA_Editing <- CA(SD_CA_Editing,
graph = FALSE)
##################################
# Obtaining the CA eigenvalues
##################################
(DR_CA_Editing_EV <- get_eigenvalue(DR_CA_Editing))## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 0.2584184 64.00355 64.00355
## Dim.2 0.1453380 35.99645 100.00000##################################
# Formulating the Scree Plot
# for the variances
##################################
(DR_CA_Editing_VarianceScreePlot <- fviz_eig(DR_CA_Editing,
addlabels = TRUE,
ylim = c(0, 100),
choice = c("variance")) +
labs(title = "Correspondence Analysis : Scree Plot of Explained Variances (Editing)",
subtitle = "Top 2 Principal Components",
y = "Percentage of Explained Variances",
x = "Principal Components") +
theme_classic())
##################################
# Formulating the Scree Plot
# for the eigenvalues
##################################
(DR_CA_Editing_EigenvalueScreePlot <- fviz_eig(DR_CA_Editing,
addlabels = TRUE,
ylim = c(0, 6),
choice = c("eigenvalue")) +
labs(title = "Correspondence Analysis : Scree Plot of Eigenvalues (Editing)",
subtitle = "Top 2 Principal Components",
y = "Eigenvalues",
x = "Principal Components") +
theme_classic())
##################################
# Extracting the CA
# results for row descriptor variables
##################################
(DR_CA_Editing_ROW <- get_ca_row(DR_CA_Editing))## Correspondence Analysis - Results for rows
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the rows"
## 2 "$cos2" "Cos2 for the rows"
## 3 "$contrib" "contributions of the rows"
## 4 "$inertia" "Inertia of the rows"##################################
# Extracting the coordinates
# representing the loadings
# for the row descriptor variabless
##################################
DR_CA_Editing_ROW$coord## Dim 1 Dim 2
## Action 0.56704105 -0.13820733
## Adventure -0.16441566 -0.52858184
## Biography 0.28198554 -0.15808970
## Comedy -0.16637971 -0.09681112
## Crime 0.08300400 -1.19003666
## Drama -0.48111282 0.31808033
## Family -0.65925497 0.79432780
## History 0.09450411 0.11971026
## LGBTQ+ -0.16441566 -0.52858184
## Music 1.86860879 0.29193192
## Musical -0.41183532 0.13287298
## Romance -0.51080318 0.39745491
## Sci-Fi 0.43078594 -0.03459231
## Thriller -0.16441566 -0.52858184
## War 1.17478794 0.58289460
## Western -0.28812549 -0.19785443##################################
# Extracting the quality of representation
# for the row descriptor variables
# on the factor map
##################################
DR_CA_Editing_ROW$cos2## Dim 1 Dim 2
## Action 0.943924837 0.056075163
## Adventure 0.088217200 0.911782800
## Biography 0.760857495 0.239142505
## Comedy 0.747065329 0.252934671
## Crime 0.004841385 0.995158615
## Drama 0.695846312 0.304153688
## Family 0.407871452 0.592128548
## History 0.383939061 0.616060939
## LGBTQ+ 0.088217200 0.911782800
## Music 0.976173866 0.023826134
## Musical 0.905719893 0.094280107
## Romance 0.622883592 0.377116408
## Sci-Fi 0.993593147 0.006406853
## Thriller 0.088217200 0.911782800
## War 0.802449252 0.197550748
## Western 0.679555338 0.320444662##################################
# Extracting the contributions
# (in percentage) of the row descriptor variables
# to the principal components
##################################
DR_CA_Editing_ROW$contrib## Dim 1 Dim 2
## Action 3.9499807 0.41722700
## Adventure 0.2490655 4.57715913
## Biography 2.9304944 1.63771622
## Comedy 1.8703779 1.12596125
## Crime 0.1057972 38.66704312
## Drama 17.7721450 13.81223319
## Family 2.6695792 6.89096101
## History 0.3840037 1.09557242
## LGBTQ+ 0.2490655 4.57715913
## Music 32.1709592 1.39615846
## Musical 1.5626957 0.28923102
## Romance 4.0066662 4.31316430
## Sci-Fi 5.1294586 0.05881011
## Thriller 0.4981310 9.15431827
## War 25.4317465 11.13221503
## Western 1.0198336 0.85507033##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 1 and 2 principal components
##################################
(DR_CA_Editing_ROW_PCVariableContributors <- fviz_contrib(DR_CA_Editing,
choice = "row",
axes = 1:2) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Editing)",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 1 principal component
##################################
(DR_CA_Editing_ROW_PC1VariableContributors <- fviz_contrib(DR_CA_Editing,
choice = "row",
axes = 1) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Editing)",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 2 principal component
##################################
(DR_CA_Editing_ROW_PC2VariableContributors <- fviz_contrib(DR_CA_Editing,
choice = "row",
axes = 2) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Editing)",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the CA
# results for column descriptor variables
##################################
(DR_CA_Editing_COL <- get_ca_col(DR_CA_Editing))## Correspondence Analysis - Results for columns
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the columns"
## 2 "$cos2" "Cos2 for the columns"
## 3 "$contrib" "contributions of the columns"
## 4 "$inertia" "Inertia of the columns"##################################
# Extracting the coordinates
# representing the loadings
# for the column descriptor variabless
##################################
DR_CA_Editing_COL$coord## Dim 1 Dim 2
## NNOM -0.33513143 0.3028233
## NOM 0.04219498 -0.4536803
## WON 1.40375986 0.3937809##################################
# Extracting the quality of representation
# for the column descriptor variables
# on the factor map
##################################
DR_CA_Editing_COL$cos2## Dim 1 Dim 2
## NNOM 0.550513662 0.44948634
## NOM 0.008575927 0.99142407
## WON 0.927049751 0.07295025##################################
# Extracting the contributions
# (in percentage) of the column descriptor variables
# to the principal components
##################################
DR_CA_Editing_COL$contrib## Dim 1 Dim 2
## NNOM 21.0409876 30.54631
## NOM 0.2843353 58.44582
## WON 78.6746771 11.00786##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 1 and 2 principal components
##################################
(DR_CA_Editing_COL_PCVariableContributors <- fviz_contrib(DR_CA_Editing,
choice = "col",
axes = 1:2) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Editing)",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 1 principal component
##################################
(DR_CA_Editing_COL_PC1VariableContributors <- fviz_contrib(DR_CA_Editing,
choice = "col",
axes = 1) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Editing)",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 2 principal component
##################################
(DR_CA_Editing_COL_PC2VariableContributors <- fviz_contrib(DR_CA_Editing,
choice = "col",
axes = 2) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Editing)",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Formulating the Symmetric Biplot
# using the row and column
# descriptor variable loadings
# for the Top 1 and Top 2 principal components
##################################
(DR_CA_SymmetricBiplot <- fviz_ca_biplot(DR_CA_Editing,
label="all",
geom = "text",
repel = TRUE) +
labs(title = "Correspondence Analysis : Symmetric Biplot (Editing)",
subtitle = "Row versus Column Descriptor Variable Loadings",
x = "Principal Component 1",
y = "Principal Component 2") +
theme_classic())
##################################
# Formulating the Asymmetric Biplot
# using the row and column
# descriptor variable loadings
# for the Top 1 and Top 2 principal components
##################################
(DR_CA_SymmetricBiplot <- fviz_ca_biplot(DR_CA_Editing,
label="all",
geom = "text",
repel = TRUE,
map = "symbiplot") +
labs(title = "Correspondence Analysis : Asymmetric Biplot (Editing)",
subtitle = "Row versus Column Descriptor Variable Loadings",
x = "Principal Component 1",
y = "Principal Component 2") +
theme_classic())
##################################
# Loading dataset for Screenplay
##################################
SD_CA_Screenplay <- Oscars.CA.Screenplay
str(SD_CA_Screenplay)## 'data.frame': 16 obs. of 3 variables:
## $ NNOM: int 2 0 4 0 0 3 0 5 0 0 ...
## $ NOM : int 2 3 7 14 5 15 2 5 1 3 ...
## $ WON : int 0 0 1 8 0 7 0 4 2 0 ...balloonplot(t(as.table(as.matrix(SD_CA_Screenplay))),
main="Screenplay by Film Genre",
xlab="Screenplay",
ylab="Genre",
label=FALSE,
show.margins=FALSE)
##################################
# Conducting a Chi-Square Test
##################################
(SD_CA_Screenplay_CHSQ <- chisq.test(SD_CA_Screenplay))##
## Pearson's Chi-squared test
##
## data: SD_CA_Screenplay
## X-squared = 41.247, df = 30, p-value = 0.08289##################################
# Performing CA
##################################
DR_CA_Screenplay <- CA(SD_CA_Screenplay,
graph = FALSE)
##################################
# Obtaining the CA eigenvalues
##################################
(DR_CA_Screenplay_EV <- get_eigenvalue(DR_CA_Screenplay))## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 0.1831592 55.95135 55.95135
## Dim.2 0.1441952 44.04865 100.00000##################################
# Formulating the Scree Plot
# for the variances
##################################
(DR_CA_Screenplay_VarianceScreePlot <- fviz_eig(DR_CA_Screenplay,
addlabels = TRUE,
ylim = c(0, 100),
choice = c("variance")) +
labs(title = "Correspondence Analysis : Scree Plot of Explained Variances (Screenplay)",
subtitle = "Top 2 Principal Components",
y = "Percentage of Explained Variances",
x = "Principal Components") +
theme_classic())
##################################
# Formulating the Scree Plot
# for the eigenvalues
##################################
(DR_CA_Screenplay_EigenvalueScreePlot <- fviz_eig(DR_CA_Screenplay,
addlabels = TRUE,
ylim = c(0, 6),
choice = c("eigenvalue")) +
labs(title = "Correspondence Analysis : Scree Plot of Eigenvalues (Screenplay)",
subtitle = "Top 2 Principal Components",
y = "Eigenvalues",
x = "Principal Components") +
theme_classic())
##################################
# Extracting the CA
# results for row descriptor variables
##################################
(DR_CA_Screenplay_ROW <- get_ca_row(DR_CA_Screenplay))## Correspondence Analysis - Results for rows
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the rows"
## 2 "$cos2" "Cos2 for the rows"
## 3 "$contrib" "contributions of the rows"
## 4 "$inertia" "Inertia of the rows"##################################
# Extracting the coordinates
# representing the loadings
# for the row descriptor variabless
##################################
DR_CA_Screenplay_ROW$coord## Dim 1 Dim 2
## Action 0.81234217 -0.17778369
## Adventure -0.33965391 -0.78144905
## Biography 0.38428571 -0.17579324
## Comedy -0.53190601 0.10529527
## Crime -0.33965391 -0.78144905
## Drama -0.21120897 0.04622376
## Family -0.33965391 -0.78144905
## History 0.33214522 0.34646817
## LGBTQ+ -0.69211609 0.84424886
## Music -0.33965391 -0.78144905
## Musical 1.19634087 0.02343809
## Romance 0.01540587 -0.05227353
## Sci-Fi 0.42834348 -0.37900548
## Thriller 0.16399685 0.84026796
## War 0.34022793 0.02741900
## Western 0.10417082 0.13002035##################################
# Extracting the quality of representation
# for the row descriptor variables
# on the factor map
##################################
DR_CA_Screenplay_ROW$cos2## Dim 1 Dim 2
## Action 0.95429251 0.045707489
## Adventure 0.15889866 0.841101339
## Biography 0.82694884 0.173051161
## Comedy 0.96229022 0.037709779
## Crime 0.15889866 0.841101339
## Drama 0.95429251 0.045707489
## Family 0.15889866 0.841101339
## History 0.47890320 0.521096802
## LGBTQ+ 0.40194025 0.598059754
## Music 0.15889866 0.841101339
## Musical 0.99961632 0.000383679
## Romance 0.07991642 0.920083582
## Sci-Fi 0.56088375 0.439116254
## Thriller 0.03669438 0.963305625
## War 0.99354715 0.006452853
## Western 0.39095067 0.609049332##################################
# Extracting the contributions
# (in percentage) of the row descriptor variables
# to the principal components
##################################
DR_CA_Screenplay_ROW$contrib## Dim 1 Dim 2
## Action 11.437701279 0.695861002
## Adventure 1.499668464 10.083266568
## Biography 7.678748880 2.041099813
## Comedy 26.970762770 1.342514688
## Crime 2.499447440 16.805444281
## Drama 4.832428790 0.294001273
## Family 0.999778976 6.722177712
## History 6.692444844 9.249822006
## LGBTQ+ 6.227014798 11.769035837
## Music 1.499668464 10.083266568
## Musical 18.605094943 0.009070776
## Romance 0.005142132 0.075199052
## Sci-Fi 7.155295654 7.115610127
## Thriller 0.699234768 23.316615710
## War 3.009483353 0.024827508
## Western 0.188084443 0.372187078##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 1 and 2 principal components
##################################
(DR_CA_Screenplay_ROW_PCVariableContributors <- fviz_contrib(DR_CA_Screenplay,
choice = "row",
axes = 1:2) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Screenplay)",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 1 principal component
##################################
(DR_CA_Screenplay_ROW_PC1VariableContributors <- fviz_contrib(DR_CA_Screenplay,
choice = "row",
axes = 1) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Screenplay)",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the row descriptor variables
# for the the Top 2 principal component
##################################
(DR_CA_Screenplay_ROW_PC2VariableContributors <- fviz_contrib(DR_CA_Screenplay,
choice = "row",
axes = 2) +
labs(title = "Correspondence Analysis : Row Descriptor Variable Contribution (Screenplay)",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the CA
# results for column descriptor variables
##################################
(DR_CA_Screenplay_COL <- get_ca_col(DR_CA_Screenplay))## Correspondence Analysis - Results for columns
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the columns"
## 2 "$cos2" "Cos2 for the columns"
## 3 "$contrib" "contributions of the columns"
## 4 "$inertia" "Inertia of the columns"##################################
# Extracting the coordinates
# representing the loadings
# for the column descriptor variabless
##################################
DR_CA_Screenplay_COL$coord## Dim 1 Dim 2
## NNOM 0.8406798 0.1617202
## NOM -0.1453620 -0.2967400
## WON -0.3716274 0.6292505##################################
# Extracting the quality of representation
# for the column descriptor variables
# on the factor map
##################################
DR_CA_Screenplay_COL$cos2## Dim 1 Dim 2
## NNOM 0.9643149 0.03568505
## NOM 0.1935263 0.80647369
## WON 0.2585967 0.74140333##################################
# Extracting the contributions
# (in percentage) of the column descriptor variables
# to the principal components
##################################
DR_CA_Screenplay_COL$contrib## Dim 1 Dim 2
## NNOM 76.560016 3.598714
## NOM 6.683833 35.379659
## WON 16.756151 61.021626##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 1 and 2 principal components
##################################
(DR_CA_Screenplay_COL_PCVariableContributors <- fviz_contrib(DR_CA_Screenplay,
choice = "col",
axes = 1:2) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Screenplay)",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 1 principal component
##################################
(DR_CA_Screenplay_COL_PC1VariableContributors <- fviz_contrib(DR_CA_Screenplay,
choice = "col",
axes = 1) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Screenplay)",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the column descriptor variables
# for the the Top 2 principal component
##################################
(DR_CA_Screenplay_COL_PC2VariableContributors <- fviz_contrib(DR_CA_Screenplay,
choice = "col",
axes = 2) +
labs(title = "Correspondence Analysis : Column Descriptor Variable Contribution (Screenplay)",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Formulating the Symmetric Biplot
# using the row and column
# descriptor variable loadings
# for the Top 1 and Top 2 principal components
##################################
(DR_CA_SymmetricBiplot <- fviz_ca_biplot(DR_CA_Screenplay,
label="all",
geom = "text",
repel = TRUE) +
labs(title = "Correspondence Analysis : Symmetric Biplot (Screenplay)",
subtitle = "Row versus Column Descriptor Variable Loadings",
x = "Principal Component 1",
y = "Principal Component 2") +
theme_classic())
##################################
# Formulating the Asymmetric Biplot
# using the row and column
# descriptor variable loadings
# for the Top 1 and Top 2 principal components
##################################
(DR_CA_SymmetricBiplot <- fviz_ca_biplot(DR_CA_Screenplay,
label="all",
geom = "text",
repel = TRUE,
map = "symbiplot") +
labs(title = "Correspondence Analysis : Asymmetric Biplot (Screenplay)",
subtitle = "Row versus Column Descriptor Variable Loadings",
x = "Principal Component 1",
y = "Principal Component 2") +
theme_classic())
1.5.3 Multiple Correspondence Analysis (MCA)
Multiple Correspondence Analysis performs a series of transformations which allows for the computation of the coordinates of the categories of the qualitative variables, as well as the coordinates of the observations in a representation space that is optimal for a criterion based on inertia. The method, which is a generalization of the Correspondence Analysis (CA) to multiple qualitative variables, assigns optimal scale values (category quantifications) to each category of each variable in such a way that overall, on average, the categories have maximum spread. Because categories of a variable receive as many scorings as there are dimensions, the variables in the analysis are assumed to be multiple nominal in optimal scaling level. It also assigns scores to the objects in the analysis in such a way that the category quantifications are the averages, or centroids, of the object scores of objects in that category. The resulting solution shows objects within the same category plotted close together and objects in different categories plotted far apart. Each object is as close as possible to the category points of categories that apply to the object. In this way, the categories divide the objects into homogeneous subgroups. Variables are considered homogeneous when they classify objects in the same categories into the same subgroups.
[A] The percentage contributions for each principal component derived from the analysis in explaining the variance in the dataset are given as follows:
[A.1] PC1 = 20%
[A.2] Combined PC1 and PC2 = 37%
[A.3] Combined PC1, PC2 and PC3 = 52%
[B] Due to the high number of descriptors and levels, no eigenvalue was sufficiently greater than 1. Nevertheless, all subsequent analysis was only proceeded for PC1 and PC2.
[C] PC1 can be described as having been collectively awarded in the directing and cinematography categories, as characterized by the following descriptor variables, ranked based on contribution:
[C.1] Directing=WON = 31.74%
[C.2] Cinematography=WON = 13.58%
[D] PC2 can be described as having been awarded in the editing category but was not nominated in the screenplay category, as characterized by the following descriptor variables, ranked based on contribution:
[D.1] Screenplay=NNOM = 29.12%
[D.2] Editing=WON = 18.01%
[E] With both PC1 and PC2 considered,the following relationships were observed among descriptor variables:
[E.1] The most represented descriptor variables and their corresponding levels are as follows:
[E.1.1] Directing=WON
[E.1.2] Cinematography=WON
[E.1.3] Screenplay=NNOM
[E.1.4] Editing=WON
[E.2] Descriptor variables demonstrated correlation and clustered around two groups:
[E.2.1] Cluster 1 (Directing=WON, Cinematography=WON) indicates that winning the directing award is associated with equally winning the cinematography.
[E.2.2] Cluster 2 (Editing=WON, Screenplay=NNOM) indicates that winners awarded with best in editing will not be nominated for screenplay.
[F] With both PC1 and PC2 considered,the following relationships were observed among individual instances:
[F.1] Movies which won for direction also won for cinematography (e.g. Life of Pi, Gravity, Birdman or (The Unexpected Virtue of Ignorance), The Revenant, La La Land and Roma).
[F.2] Movies which won for editing are most associated with the absence of a nomination for screenplay (e.g. Gravity, Mad Max: Fury Road, Hacksaw Ridge, Dunkirk, Bohemian Rhapsody and Ford v Ferrari).
##################################
# Loading dataset
##################################
SD_MCA <- Oscars.MCA
str(SD_MCA)## 'data.frame': 126 obs. of 6 variables:
## $ Cinematography: Factor w/ 3 levels "NNOM","NOM","WON": 3 1 1 1 2 2 1 1 1 1 ...
## $ Directing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 1 1 3 2 2 1 1 2 ...
## $ Editing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 2 1 3 2 2 1 1 1 ...
## $ Screenplay : Factor w/ 3 levels "NNOM","NOM","WON": 1 1 2 2 3 2 3 2 2 2 ...
## $ Year : Factor w/ 14 levels "2010","2011",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Picture : Factor w/ 2 levels "NOM","WON": 1 1 1 1 2 1 1 1 1 1 ...##################################
# Performing MCA
##################################
DR_MCA <- MCA(SD_MCA[,c(1:4)],
graph = FALSE)
##################################
# Obtaining the MCA eigenvalues
##################################
(DR_MCA_EV <- get_eigenvalue(DR_MCA))## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 0.4014500 20.072501 20.07250
## Dim.2 0.3482608 17.413038 37.48554
## Dim.3 0.2934227 14.671133 52.15667
## Dim.4 0.2814318 14.071589 66.22826
## Dim.5 0.2191032 10.955162 77.18342
## Dim.6 0.1864147 9.320736 86.50416
## Dim.7 0.1647588 8.237939 94.74210
## Dim.8 0.1051580 5.257902 100.00000##################################
# Formulating the Scree Plot
# for the variances
##################################
(DR_MCA_VarianceScreePlot <- fviz_eig(DR_MCA,
addlabels = TRUE,
ylim = c(0, 100),
choice = c("variance")) +
labs(title = "Multiple Correspondence Analysis : Scree Plot of Explained Variances",
subtitle = "Top 2 Principal Components",
y = "Percentage of Explained Variances",
x = "Principal Components") +
theme_classic())
##################################
# Formulating the Scree Plot
# for the eigenvalues
##################################
(DR_MCA_EigenvalueScreePlot <- fviz_eig(DR_MCA,
addlabels = TRUE,
ylim = c(0, 6),
choice = c("eigenvalue")) +
labs(title = "Multiple Correspondence Analysis : Scree Plot of Eigenvalues",
subtitle = "Top 2 Principal Components",
y = "Eigenvalues",
x = "Principal Components") +
theme_classic())
##################################
# Extracting the MCA
# descriptor variable loadings
##################################
DR_MCA_VAR <- get_mca_var(DR_MCA)
##################################
# Extracting the coordinates
# representing the loadings
# for the descriptor variables
##################################
DR_MCA_VAR$coord## Dim 1 Dim 2 Dim 3 Dim 4
## Cinematography_NNOM -0.5220182052 -0.1264760 0.12785667 0.38942121
## Cinematography_NOM 0.6927420866 -0.1325546 0.28326894 -1.19605797
## Cinematography_WON 1.4539205813 1.1147985 -1.50587760 0.63970892
## Directing_NNOM -0.6590730961 0.3732744 -0.19240706 0.23562263
## Directing_NOM 0.1678869817 -0.5334948 0.37577191 -0.49146594
## Directing_WON 2.1419501885 0.4465739 -0.61170677 0.86756855
## Editing_NNOM -0.5971330422 0.3091986 -0.24548152 -0.12141930
## Editing_NOM 0.5111151354 -0.7525933 -0.07146831 0.05150745
## Editing_WON 0.7574714257 1.5595180 1.43774806 0.36370692
## Screenplay_NNOM -0.0009048548 1.4299445 0.50282891 -0.74923832
## Screenplay_NOM -0.1076851566 -0.3010392 -0.60515086 -0.15377497
## Screenplay_WON 0.2815584929 -0.4918838 1.12876035 1.06987609
## Dim 5
## Cinematography_NNOM 0.003994189
## Cinematography_NOM -0.489028350
## Cinematography_WON 1.216800033
## Directing_NNOM -0.554851077
## Directing_NOM 0.712251511
## Directing_WON -0.358079754
## Editing_NNOM 0.459427895
## Editing_NOM -0.341356193
## Editing_WON -0.790352271
## Screenplay_NNOM 0.251177034
## Screenplay_NOM -0.230016943
## Screenplay_WON 0.375421821##################################
# Extracting the quality of representation
# for the descriptor variables
# on the factor map
##################################
DR_MCA_VAR$cos2## Dim 1 Dim 2 Dim 3 Dim 4
## Cinematography_NNOM 4.739183e-01 0.027819444 0.028430136 0.263737183
## Cinematography_NOM 1.702841e-01 0.006234768 0.028472717 0.507616171
## Cinematography_WON 2.431903e-01 0.142974205 0.260882083 0.047079271
## Directing_NNOM 3.825114e-01 0.122696917 0.032600122 0.048889005
## Directing_NOM 2.046384e-02 0.206639535 0.102518359 0.175363763
## Directing_WON 5.734938e-01 0.024928533 0.046773147 0.094084398
## Editing_NNOM 3.346252e-01 0.089720491 0.056552798 0.013835406
## Editing_NOM 1.835731e-01 0.398008472 0.003589208 0.001864282
## Editing_WON 6.600813e-02 0.279798703 0.237810207 0.015218367
## Screenplay_NNOM 2.026639e-07 0.506124052 0.062583394 0.138950015
## Screenplay_NOM 1.597198e-02 0.124822588 0.504399092 0.032570039
## Screenplay_WON 2.265005e-02 0.069128491 0.364028552 0.327038529
## Dim 5
## Cinematography_NNOM 0.0000277453
## Cinematography_NOM 0.0848592258
## Cinematography_WON 0.1703347802
## Directing_NNOM 0.2711003480
## Directing_NOM 0.3683153067
## Directing_WON 0.0160276388
## Editing_NNOM 0.1980848216
## Editing_NOM 0.0818817653
## Editing_WON 0.0718631616
## Screenplay_NNOM 0.0156163125
## Screenplay_NOM 0.0728729994
## Screenplay_WON 0.0402690125##################################
# Extracting the contributions
# (in percentage) of the descriptor variables
# to the principal components
##################################
DR_MCA_VAR$contrib## Dim 1 Dim 2 Dim 3 Dim 4 Dim 5
## Cinematography_NNOM 1.077455e+01 0.7290733 0.8843264 8.55313892 0.001155761
## Cinematography_NOM 7.826995e+00 0.3303453 1.7905550 33.28240706 7.146652781
## Cinematography_WON 1.358197e+01 9.2045183 19.9341857 3.75063238 17.430203052
## Directing_NNOM 1.266652e+01 4.6835308 1.4769637 2.30931050 16.448471491
## Directing_NOM 7.383255e-01 8.5941159 5.0605801 9.02524596 24.348000197
## Directing_WON 3.174569e+01 1.5906685 3.5423414 7.42902749 1.625579588
## Editing_NNOM 1.075004e+01 3.3225378 2.4856688 0.63401803 11.659642215
## Editing_NOM 6.713961e+00 16.7798845 0.1795999 0.09726122 5.487058437
## Editing_WON 3.686497e+00 18.0131253 18.1712472 1.21239133 7.353691928
## Screenplay_NNOM 1.011663e-05 29.1234808 4.2742143 9.89410016 1.428303605
## Screenplay_NOM 4.183816e-01 3.7690681 18.0769838 1.21699970 3.497543972
## Screenplay_WON 1.097067e+00 3.8596514 24.1233338 22.59546726 3.573696974##################################
# Extracting the quality of representation
# for the descriptor variables
# on the factor map
##################################
(DR_MCA_VariableSquaredCorrelationCircle <- fviz_mca_var(DR_MCA,
col.var = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
legend.title = "Squared Coordinates") +
labs(title = "Multiple Correspondence Analysis : Squared Coordinate Plot",
subtitle = "Descriptor Variable Representation Quality",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Formulating clusters of the
# descriptor variables
##################################
set.seed(123)
DR_MCA_KMEANS <- kmeans(DR_MCA_VAR$coord, centers=3, nstart=25)
DR_MCA_KMEANS_CLUSTER <- as.factor(DR_MCA_KMEANS$cluster)
##################################
# Extracting the correlation
# between the descriptor variables
# and top principal components
##################################
(DR_MCA_VariableCorrelationCircle <- fviz_mca_var(DR_MCA,
col.var = DR_MCA_KMEANS_CLUSTER,
palette = c("#0073C2FF", "#EFC000FF", "#868686FF"),
legend.title = "Cluster") +
labs(title = "Multiple Correspondence Analysis : Factorial Map of Qualitative Variables",
subtitle = "Principal Components Versus Descriptor Variable Clusters",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Extracting the contribution
# of the descriptor variables
# for the the Top 1 and 2 principal components
##################################
(DR_MCA_PCVariableContributors <- fviz_contrib(DR_MCA,
choice = "var",
axes = 1:2) +
labs(title = "Multiple Correspondence Analysis : Descriptor Variable Contribution",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Testing the statistical significance
# of the contribution
# of the descriptor variables
# for the the Top 1 and 2 principal components
##################################
DR_MCA_VariableContributionTest <- dimdesc(DR_MCA,
axes = c(1,2),
proba = 0.05)
##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 1 principal component
##################################
(DR_MCA_PC1VariableContributors <- fviz_contrib(DR_MCA,
choice = "var",
axes = 1) +
labs(title = "Multiple Correspondence Analysis : Descriptor Variable Contribution",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Testing the statistical significance
# of the contribution
# of the descriptor variables
# for the Top 1 principal component
##################################
DR_MCA_VariableContributionTest$'Dim 1'##
## Link between the variable and the categorical variable (1-way anova)
## =============================================
## R2 p.value
## Directing 0.7250272 3.283334e-35
## Cinematography 0.5168029 3.746658e-20
## Editing 0.3396347 8.255279e-12
##
## Link between variable abd the categories of the categorical variables
## ================================================================
## Estimate p.value
## Directing=Directing_WON 1.0084996 1.066429e-24
## Cinematography=Cinematography_WON 0.5780799 4.450536e-09
## Editing=Editing_NOM 0.1820318 5.586469e-07
## Cinematography=Cinematography_NOM 0.0957966 1.573813e-06
## Editing=Editing_WON 0.3381234 3.683149e-03
## Editing=Editing_NNOM -0.5201552 1.304909e-12
## Directing=Directing_NNOM -0.7662311 1.192963e-14
## Cinematography=Cinematography_NNOM -0.6738765 5.224619e-19##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 2 principal component
##################################
(DR_MCA_PC2VariableContributors <- fviz_contrib(DR_MCA,
choice = "var",
axes = 2) +
labs(title = "Multiple Correspondence Analysis : Descriptor Variable Contribution",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Testing the statistical significance
# of the contribution
# of the descriptor variables
# for the Top 2 principal component
##################################
DR_MCA_VariableContributionTest$'Dim 2'##
## Link between the variable and the categorical variable (1-way anova)
## =============================================
## R2 p.value
## Editing 0.5309660 6.012674e-21
## Screenplay 0.5119740 6.906284e-20
## Directing 0.2071220 6.326897e-07
## Cinematography 0.1429811 7.566777e-05
##
## Link between variable abd the categories of the categorical variables
## ================================================================
## Estimate p.value
## Screenplay=Screenplay_NNOM 0.71855222 1.007469e-20
## Editing=Editing_WON 0.70077312 1.925781e-10
## Cinematography=Cinematography_WON 0.48954310 1.269630e-05
## Directing=Directing_NNOM 0.16395356 5.798540e-05
## Screenplay=Screenplay_WON -0.41558827 2.935568e-03
## Editing=Editing_NNOM -0.03708562 6.560151e-04
## Screenplay=Screenplay_NOM -0.30296395 4.950520e-05
## Directing=Directing_NOM -0.37116380 8.944524e-08
## Editing=Editing_NOM -0.66368750 2.420712e-15##################################
# Extracting the MCA individual scores
##################################
DR_MCA_IND <- get_mca_ind(DR_MCA)
##################################
# Extracting the coordinates
# representing the scores
# for the individuals
##################################
DR_MCA_IND$coord[,c("Dim 1","Dim 2")]## Dim 1 Dim 2
## Avatar 0.84123067 0.53320524
## The Blind Side -0.70199134 0.84130641
## District 9 -0.30684197 -0.34179995
## An Education -0.74412366 0.10800804
## The Hurt Locker 1.52845528 0.58531128
## Inglourious Basterds 0.49876001 -0.72851058
## Precious: Based on the Novel 'Push' by Sapphire 0.17303576 -0.80678321
## A Serious Man -0.74412366 0.10800804
## Up -0.74412366 0.10800804
## Up in the Air -0.41782987 -0.27612752
## Black Swan 0.54089234 0.00478779
## The Fighter 0.01945182 -0.72593552
## Inception 0.03552287 0.63385043
## The Kids Are All Right -0.74412366 0.10800804
## The King's Speech 1.43125043 -0.39417077
## 127 Hours -0.30684197 -0.34179995
## The Social Network 0.74954880 0.17012377
## Toy Story 3 -0.74412366 0.10800804
## True Grit 0.06147832 -0.27870259
## Winter's Bone -0.74412366 0.10800804
## The Artist 1.27766650 -0.31332307
## The Descendants 0.17303576 -0.80678321
## Extremely Loud & Incredibly Close -0.70199134 0.84130641
## The Help -0.70199134 0.84130641
## Hugo 0.79909835 -0.20009313
## Midnight in Paris -0.26424593 -0.35697522
## Moneyball -0.30684197 -0.34179995
## The Tree of Life 0.10361065 0.45459578
## War Horse -0.22268314 0.83873134
## Amour -0.41782987 -0.27612752
## Argo -0.05605319 0.55683439
## Beasts of the Southern Wild -0.41782987 -0.27612752
## Django Unchained -0.11123153 0.02458528
## Les Miserables -0.70199134 0.84130641
## Life of Pi 1.57800484 0.21509438
## Lincoln 0.49876001 -0.72851058
## Silver Linings Playbook 0.01945182 -0.72593552
## Zero Dark Thirty -0.30684197 -0.34179995
## American Hustle 0.01945182 -0.72593552
## Captain Phillips -0.30684197 -0.34179995
## Dallas Buyers Club -0.30684197 -0.34179995
## Gravity 1.71734201 1.92787479
## Her -0.59053972 0.02716034
## Nebraska 0.06147832 -0.27870259
## Philomena -0.74412366 0.10800804
## 12 Years a Slave 0.17303576 -0.80678321
## The Wolf of Wall Street -0.41782987 -0.27612752
## American Sniper -0.30684197 -0.34179995
## Birdman or (The Unexpected Virtue of Ignorance) 1.29430709 0.58405467
## Boyhood 0.01945182 -0.72593552
## The Grand Budapest Hotel 0.49876001 -0.72851058
## The Imitation Game 0.17303576 -0.80678321
## Selma -0.70199134 0.84130641
## The Theory of Everything -0.74412366 0.10800804
## Whiplash -0.20963712 0.63768209
## The Big Short 0.17303576 -0.80678321
## Bridge of Spies -0.74412366 0.10800804
## Brooklyn -0.74412366 0.10800804
## Mad Max: Fury Road 0.63809718 0.98426984
## The Martian -0.74412366 0.10800804
## The Revenant 1.62013716 0.94839275
## Room -0.41782987 -0.27612752
## Spotlight 0.17303576 -0.80678321
## Arrival 0.49876001 -0.72851058
## Fences -0.74412366 0.10800804
## Hacksaw Ridge 0.15878899 0.98684490
## Hell or High Water -0.30684197 -0.34179995
## Hidden Figures -0.74412366 0.10800804
## La La Land 1.57800484 0.21509438
## Lion -0.26481547 0.10543298
## Manchester by the Sea -0.26424593 -0.35697522
## Moonlight 0.65234395 -0.80935828
## Call Me by Your Name -0.59053972 0.02716034
## Darkest Hour -0.22268314 0.83873134
## Dunkirk 0.63809718 0.98426984
## Get Out -0.26424593 -0.35697522
## Lady Bird -0.41782987 -0.27612752
## Phantom Thread -0.37569755 0.45717084
## The Post -0.70199134 0.84130641
## The Shape of Water 1.27766650 -0.31332307
## Three Billboards outside Ebbing, Missouri -0.30684197 -0.34179995
## Black Panther -0.70199134 0.84130641
## BlacKkKlansman 0.17303576 -0.80678321
## Bohemian Rhapsody -0.16750480 1.37098046
## The Favourite 0.49876001 -0.72851058
## Green Book -0.15325803 -0.42264765
## Roma 1.14072315 0.66490237
## A Star Is Born -0.26481547 0.10543298
## Vice 0.01945182 -0.72593552
## Ford v Ferrari -0.16750480 1.37098046
## The Irishman 0.49876001 -0.72851058
## Jojo Rabbit -0.15325803 -0.42264765
## Joker 0.49876001 -0.72851058
## Little Women -0.74412366 0.10800804
## Marriage Story -0.74412366 0.10800804
## 1917 0.36181666 0.24971486
## Once upon a Time...in Hollywood 0.06147832 -0.27870259
## Parasite 0.95194224 -0.39159571
## The Father -0.15325803 -0.42264765
## Judas and the Black Messiah -0.26481547 0.10543298
## Mank 0.40394899 0.98301323
## Minari -0.41782987 -0.27612752
## Nomadland 1.27766650 -0.31332307
## Promising Young Woman 0.17303576 -0.80678321
## Sound of Metal -0.20963712 0.63768209
## The Trial of the Chicago 7 0.17246622 -0.34437502
## Belfast -0.26424593 -0.35697522
## CODA -0.59053972 0.02716034
## Don't Look Up -0.30684197 -0.34179995
## Drive My Car -0.41782987 -0.27612752
## Dune 0.57000941 1.16352448
## King Richard -0.30684197 -0.34179995
## Licorice Pizza -0.41782987 -0.27612752
## Nightmare Alley -0.22268314 0.83873134
## The Power of the Dog 1.27766650 -0.31332307
## West Side Story 0.10361065 0.45459578
## All Quiet on the Western Front 0.03552287 0.63385043
## Avatar: The Way of Water -0.70199134 0.84130641
## The Banshees of Inisherin 0.01945182 -0.72593552
## Elvis 0.21459854 0.38892335
## Everything Everywhere All at Once 1.04914709 0.58788634
## The Fabelmans -0.41782987 -0.27612752
## Tar 0.49876001 -0.72851058
## Top Gun: Maverick -0.30684197 -0.34179995
## Triangle of Sadness -0.41782987 -0.27612752
## Women Talking -0.59053972 0.02716034##################################
# Extracting the quality of representation
# for the individuals
# on the factor map
##################################
DR_MCA_IND$cos2[,c("Dim 1","Dim 2")]## Dim 1 Dim 2
## Avatar 0.1822392975 7.321510e-02
## The Blind Side 0.2891900021 4.153633e-01
## District 9 0.0975744805 1.210740e-01
## An Education 0.6324263704 1.332392e-02
## The Hurt Locker 0.4061061887 5.955359e-02
## Inglourious Basterds 0.1568324557 3.345988e-01
## Precious: Based on the Novel 'Push' by Sapphire 0.0174193322 3.786810e-01
## A Serious Man 0.6324263704 1.332392e-02
## Up 0.6324263704 1.332392e-02
## Up in the Air 0.1865210265 8.146072e-02
## Black Swan 0.1211620717 9.493257e-06
## The Fighter 0.0003690130 5.139458e-01
## Inception 0.0004343988 1.383076e-01
## The Kids Are All Right 0.6324263704 1.332392e-02
## The King's Speech 0.5205372305 3.948111e-02
## 127 Hours 0.0975744805 1.210740e-01
## The Social Network 0.1371317088 7.064282e-03
## Toy Story 3 0.6324263704 1.332392e-02
## True Grit 0.0025251344 5.189464e-02
## Winter's Bone 0.6324263704 1.332392e-02
## The Artist 0.5035538379 3.028277e-02
## The Descendants 0.0174193322 3.786810e-01
## Extremely Loud & Incredibly Close 0.2891900021 4.153633e-01
## The Help 0.2891900021 4.153633e-01
## Hugo 0.2090417116 1.310680e-02
## Midnight in Paris 0.0428515726 7.820352e-02
## Moneyball 0.0975744805 1.210740e-01
## The Tree of Life 0.0046167227 8.887422e-02
## War Horse 0.0218946344 3.106052e-01
## Amour 0.1865210265 8.146072e-02
## Argo 0.0009039724 8.920859e-02
## Beasts of the Southern Wild 0.1865210265 8.146072e-02
## Django Unchained 0.0058091073 2.837944e-04
## Les Miserables 0.2891900021 4.153633e-01
## Life of Pi 0.5286438743 9.822107e-03
## Lincoln 0.1568324557 3.345988e-01
## Silver Linings Playbook 0.0003690130 5.139458e-01
## Zero Dark Thirty 0.0975744805 1.210740e-01
## American Hustle 0.0003690130 5.139458e-01
## Captain Phillips 0.0975744805 1.210740e-01
## Dallas Buyers Club 0.0975744805 1.210740e-01
## Gravity 0.4009246716 5.052506e-01
## Her 0.2222612387 4.701495e-04
## Nebraska 0.0025251344 5.189464e-02
## Philomena 0.6324263704 1.332392e-02
## 12 Years a Slave 0.0174193322 3.786810e-01
## The Wolf of Wall Street 0.1865210265 8.146072e-02
## American Sniper 0.0975744805 1.210740e-01
## Birdman or (The Unexpected Virtue of Ignorance) 0.3152206556 6.418699e-02
## Boyhood 0.0003690130 5.139458e-01
## The Grand Budapest Hotel 0.1568324557 3.345988e-01
## The Imitation Game 0.0174193322 3.786810e-01
## Selma 0.2891900021 4.153633e-01
## The Theory of Everything 0.6324263704 1.332392e-02
## Whiplash 0.0157958513 1.461555e-01
## The Big Short 0.0174193322 3.786810e-01
## Bridge of Spies 0.6324263704 1.332392e-02
## Brooklyn 0.6324263704 1.332392e-02
## Mad Max: Fury Road 0.0962125874 2.289215e-01
## The Martian 0.6324263704 1.332392e-02
## The Revenant 0.4738973318 1.623892e-01
## Room 0.1865210265 8.146072e-02
## Spotlight 0.0174193322 3.786810e-01
## Arrival 0.1568324557 3.345988e-01
## Fences 0.6324263704 1.332392e-02
## Hacksaw Ridge 0.0068681011 2.652734e-01
## Hell or High Water 0.0975744805 1.210740e-01
## Hidden Figures 0.6324263704 1.332392e-02
## La La Land 0.5286438743 9.822107e-03
## Lion 0.0488234219 7.739171e-03
## Manchester by the Sea 0.0428515726 7.820352e-02
## Moonlight 0.1866741937 2.873509e-01
## Call Me by Your Name 0.2222612387 4.701495e-04
## Darkest Hour 0.0218946344 3.106052e-01
## Dunkirk 0.0962125874 2.289215e-01
## Get Out 0.0428515726 7.820352e-02
## Lady Bird 0.1865210265 8.146072e-02
## Phantom Thread 0.0799943330 1.184512e-01
## The Post 0.2891900021 4.153633e-01
## The Shape of Water 0.5035538379 3.028277e-02
## Three Billboards outside Ebbing, Missouri 0.0975744805 1.210740e-01
## Black Panther 0.2891900021 4.153633e-01
## BlacKkKlansman 0.0174193322 3.786810e-01
## Bohemian Rhapsody 0.0077706989 5.205568e-01
## The Favourite 0.1568324557 3.345988e-01
## Green Book 0.0141629138 1.077117e-01
## Roma 0.2815961296 9.567136e-02
## A Star Is Born 0.0488234219 7.739171e-03
## Vice 0.0003690130 5.139458e-01
## Ford v Ferrari 0.0077706989 5.205568e-01
## The Irishman 0.1568324557 3.345988e-01
## Jojo Rabbit 0.0141629138 1.077117e-01
## Joker 0.1568324557 3.345988e-01
## Little Women 0.6324263704 1.332392e-02
## Marriage Story 0.6324263704 1.332392e-02
## 1917 0.0441474907 2.102895e-02
## Once upon a Time...in Hollywood 0.0025251344 5.189464e-02
## Parasite 0.2685401891 4.544268e-02
## The Father 0.0141629138 1.077117e-01
## Judas and the Black Messiah 0.0488234219 7.739171e-03
## Mank 0.0430107950 2.547083e-01
## Minari 0.1865210265 8.146072e-02
## Nomadland 0.5035538379 3.028277e-02
## Promising Young Woman 0.0174193322 3.786810e-01
## Sound of Metal 0.0157958513 1.461555e-01
## The Trial of the Chicago 7 0.0194954517 7.772997e-02
## Belfast 0.0428515726 7.820352e-02
## CODA 0.2222612387 4.701495e-04
## Don't Look Up 0.0975744805 1.210740e-01
## Drive My Car 0.1865210265 8.146072e-02
## Dune 0.0675271205 2.813619e-01
## King Richard 0.0975744805 1.210740e-01
## Licorice Pizza 0.1865210265 8.146072e-02
## Nightmare Alley 0.0218946344 3.106052e-01
## The Power of the Dog 0.5035538379 3.028277e-02
## West Side Story 0.0046167227 8.887422e-02
## All Quiet on the Western Front 0.0004343988 1.383076e-01
## Avatar: The Way of Water 0.2891900021 4.153633e-01
## The Banshees of Inisherin 0.0003690130 5.139458e-01
## Elvis 0.0195617540 6.425135e-02
## Everything Everywhere All at Once 0.2120081487 6.656816e-02
## The Fabelmans 0.1865210265 8.146072e-02
## Tar 0.1568324557 3.345988e-01
## Top Gun: Maverick 0.0975744805 1.210740e-01
## Triangle of Sadness 0.1865210265 8.146072e-02
## Women Talking 0.2222612387 4.701495e-04##################################
# Extracting the contributions
# (in percentage) of the individuals
# to the principal components
##################################
DR_MCA_IND$contrib[,c("Dim 1","Dim 2")]## Dim 1 Dim 2
## Avatar 1.399033677 6.479086e-01
## The Blind Side 0.974229942 1.612996e+00
## District 9 0.186134766 2.662373e-01
## An Education 1.094682550 2.658503e-02
## The Hurt Locker 4.618526525 7.807261e-01
## Inglourious Basterds 0.491791730 1.209474e+00
## Precious: Based on the Novel 'Push' by Sapphire 0.059192909 1.483333e+00
## A Serious Man 1.094682550 2.658503e-02
## Up 1.094682550 2.658503e-02
## Up in the Air 0.345141303 1.737578e-01
## Black Swan 0.578388464 5.223903e-05
## The Fighter 0.000748029 1.200939e+00
## Inception 0.002494676 9.155846e-01
## The Kids Are All Right 1.094682550 2.658503e-02
## The King's Speech 4.049759486 3.540738e-01
## 127 Hours 0.186134766 2.662373e-01
## The Social Network 1.110702608 6.595609e-02
## Toy Story 3 1.094682550 2.658503e-02
## True Grit 0.007472088 1.770137e-01
## Winter's Bone 1.094682550 2.658503e-02
## The Artist 3.227252762 2.237225e-01
## The Descendants 0.059192909 1.483333e+00
## Extremely Loud & Incredibly Close 0.974229942 1.612996e+00
## The Help 0.974229942 1.612996e+00
## Hugo 1.262404218 9.124084e-02
## Midnight in Paris 0.138043062 2.904030e-01
## Moneyball 0.186134766 2.662373e-01
## The Tree of Life 0.021222998 4.709510e-01
## War Horse 0.098033082 1.603137e+00
## Amour 0.345141303 1.737578e-01
## Argo 0.006211530 7.066055e-01
## Beasts of the Southern Wild 0.345141303 1.737578e-01
## Django Unchained 0.024459849 1.377448e-03
## Les Miserables 0.974229942 1.612996e+00
## Life of Pi 4.922827606 1.054346e-01
## Lincoln 0.491791730 1.209474e+00
## Silver Linings Playbook 0.000748029 1.200939e+00
## Zero Dark Thirty 0.186134766 2.662373e-01
## American Hustle 0.000748029 1.200939e+00
## Captain Phillips 0.186134766 2.662373e-01
## Dallas Buyers Club 0.186134766 2.662373e-01
## Gravity 5.830577249 8.469984e+00
## Her 0.689439557 1.681107e-03
## Nebraska 0.007472088 1.770137e-01
## Philomena 1.094682550 2.658503e-02
## 12 Years a Slave 0.059192909 1.483333e+00
## The Wolf of Wall Street 0.345141303 1.737578e-01
## American Sniper 0.186134766 2.662373e-01
## Birdman or (The Unexpected Virtue of Ignorance) 3.311865001 7.773774e-01
## Boyhood 0.000748029 1.200939e+00
## The Grand Budapest Hotel 0.491791730 1.209474e+00
## The Imitation Game 0.059192909 1.483333e+00
## Selma 0.974229942 1.612996e+00
## The Theory of Everything 1.094682550 2.658503e-02
## Whiplash 0.086882910 9.266876e-01
## The Big Short 0.059192909 1.483333e+00
## Bridge of Spies 1.094682550 2.658503e-02
## Brooklyn 1.094682550 2.658503e-02
## Mad Max: Fury Road 0.804955036 2.207767e+00
## The Martian 1.094682550 2.658503e-02
## The Revenant 5.189213436 2.049752e+00
## Room 0.345141303 1.737578e-01
## Spotlight 0.059192909 1.483333e+00
## Arrival 0.491791730 1.209474e+00
## Fences 1.094682550 2.658503e-02
## Hacksaw Ridge 0.049846967 2.219334e+00
## Hell or High Water 0.186134766 2.662373e-01
## Hidden Figures 1.094682550 2.658503e-02
## La La Land 4.922827606 1.054346e-01
## Lion 0.138638759 2.533249e-02
## Manchester by the Sea 0.138043062 2.904030e-01
## Moonlight 0.841300693 1.492817e+00
## Call Me by Your Name 0.689439557 1.681107e-03
## Darkest Hour 0.098033082 1.603137e+00
## Dunkirk 0.804955036 2.207767e+00
## Get Out 0.138043062 2.904030e-01
## Lady Bird 0.345141303 1.737578e-01
## Phantom Thread 0.279045282 4.763015e-01
## The Post 0.974229942 1.612996e+00
## The Shape of Water 3.227252762 2.237225e-01
## Three Billboards outside Ebbing, Missouri 0.186134766 2.662373e-01
## Black Panther 0.974229942 1.612996e+00
## BlacKkKlansman 0.059192909 1.483333e+00
## Bohemian Rhapsody 0.055469275 4.283388e+00
## The Favourite 0.491791730 1.209474e+00
## Green Book 0.046434894 4.070819e-01
## Roma 2.572518321 1.007490e+00
## A Star Is Born 0.138638759 2.533249e-02
## Vice 0.000748029 1.200939e+00
## Ford v Ferrari 0.055469275 4.283388e+00
## The Irishman 0.491791730 1.209474e+00
## Jojo Rabbit 0.046434894 4.070819e-01
## Joker 0.491791730 1.209474e+00
## Little Women 1.094682550 2.658503e-02
## Marriage Story 1.094682550 2.658503e-02
## 1917 0.258806450 1.421064e-01
## Once upon a Time...in Hollywood 0.007472088 1.770137e-01
## Parasite 1.791509708 3.494627e-01
## The Father 0.046434894 4.070819e-01
## Judas and the Black Messiah 0.138638759 2.533249e-02
## Mank 0.322590084 2.202134e+00
## Minari 0.345141303 1.737578e-01
## Nomadland 3.227252762 2.237225e-01
## Promising Young Woman 0.059192909 1.483333e+00
## Sound of Metal 0.086882910 9.266876e-01
## The Trial of the Chicago 7 0.058803891 2.702640e-01
## Belfast 0.138043062 2.904030e-01
## CODA 0.689439557 1.681107e-03
## Don't Look Up 0.186134766 2.662373e-01
## Drive My Car 0.345141303 1.737578e-01
## Dune 0.642335633 3.085148e+00
## King Richard 0.186134766 2.662373e-01
## Licorice Pizza 0.345141303 1.737578e-01
## Nightmare Alley 0.098033082 1.603137e+00
## The Power of the Dog 3.227252762 2.237225e-01
## West Side Story 0.021222998 4.709510e-01
## All Quiet on the Western Front 0.002494676 9.155846e-01
## Avatar: The Way of Water 0.974229942 1.612996e+00
## The Banshees of Inisherin 0.000748029 1.200939e+00
## Elvis 0.091044038 3.447093e-01
## Everything Everywhere All at Once 2.176059309 7.876108e-01
## The Fabelmans 0.345141303 1.737578e-01
## Tar 0.491791730 1.209474e+00
## Top Gun: Maverick 0.186134766 2.662373e-01
## Triangle of Sadness 0.345141303 1.737578e-01
## Women Talking 0.689439557 1.681107e-03##################################
# Extracting the correlation
# between the individual instances
# grouped by Picture categories
# and top principal components
##################################
(DR_MCA_IndividualCorrelationCircleByPicture <- fviz_mca_ind(DR_MCA,
geom.ind = "text",
col.ind = SD_MCA$Picture,
palette = c("#888888","#5544FF"),
repel = TRUE,
legend.title = "Picture",
addEllipses = FALSE) +
labs(title = "Multiple Correspondence Analysis : Factorial Map of Individuals",
subtitle = "Principal Components Versus Individuals Grouped by Picture Categories",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Extracting the correlation
# between the individual instances
# grouped by Year categories
# and top principal components
##################################
(DR_MCA_IndividualCorrelationCircleByYear <- fviz_mca_ind(DR_MCA,
geom.ind = "text",
col.ind = SD_MCA$Year,
repel = TRUE,
legend.title = "Year",
addEllipses = FALSE) +
labs(title = "Multiple Correspondence Analysis : Factorial Map of Individuals",
subtitle = "Principal Components Versus Individuals Grouped by Picture Categories",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 1 and Top 2 principal components
##################################
(DR_MCA_PCIndividualContributors <- fviz_contrib(DR_MCA,
choice = "ind",
axes = 1:2,
top = 10) +
labs(title = "Multiple Correspondence Analysis : Individual Contribution",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 1 principal component
##################################
(DR_MCA_PC1IndividualContributors <- fviz_contrib(DR_MCA,
choice = "ind",
axes = 1,
top = 10) +
labs(title = "Multiple Correspondence Analysis : Individual Contribution",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 2 principal component
##################################
(DR_MCA_PC2IndividualContributors <- fviz_contrib(DR_MCA,
choice = "ind",
axes = 2,
top = 10) +
labs(title = "Multiple Correspondence Analysis : Individual Contribution",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Formulating the Biplot
# using the individual scores
# and descriptor variable loadings
# for the Top 1 and Top 2 principal components
##################################
(DR_MCA_Biplot <- fviz_mca_biplot(DR_MCA,
label = c("var","ind"),
repel = TRUE,
habillage = SD_MCA$Picture,
palette = c("#888888","#5544FF"),
col.var = "#FF5050",
legend.title = "Picture",
addEllipses = FALSE) +
labs(title = "Multiple Correspondence Analysis : Biplot",
subtitle = "Individual Scores versus Descriptor Variable Loadings",
x = "Principal Component 1",
y = "Principal Component 2") +
theme_classic() +
theme(legend.position="top"))
1.5.4 Multiple Factor Analysis (MFA)
Multiple Factor Analysis evaluates several groups of variables simultaneously, and to obtain results, in particular, charts, that allow studying the relationship between the observations, the variables, and groups. Within a group, the variables must be of the same type (quantitative table, qualitative table or frequency table), but the groups can be of different types. The method is a synthesis of the PCA (Principal Component Analysis) for quantitative tables, the MCA (Multiple Correspondence Analysis) for qualitative tables and the CA (Correspondence Analysis) for frequency tables. The process involves successively carrying out for each table a PCA, an MCA or a CA according to the type of the variables of the table. The method stores the value of the first eigenvalue of each analysis to then weight the various tables in the second part of the analysis. A weighted PCA is carried out a on the columns of all the tables, knowing that the tables of qualitative variables are transformed into complete disjunctive tables, each indicator variable having a weight that is a function of the frequency of the corresponding category. The weighting of the tables prevents that the tables which include more variables weight too much in the analysis. The method allows visualization in a two or three-dimensional space, the groups (each group being represented by a point), the variables, the principal axes of the analyses of the first phase, and the individuals. In addition, one can study the impact of the other tables on an observation by simultaneously visualizing the observation described by all the variables and the projected observations described by the variables of only one group.
[A] Among the assigned group of descriptor variables, relationships observed are as follows:
[A.1] Association between two groups of descriptors were noted = Group=Technicalities comprised of Picture, Cinematography and Directing; and Group=Aesthetics comprised of Design and Sound.
[A.2] Group=Recognitions comprised of Nominations_Total and Nomination_SuccessRate was not associated with other groups.
[A.3] Group=Storytelling comprised of Editing, Actingand Screenplay was not associated with other groups.
[B] PC1 can be described as having been collectively awarded in all categories, as characterized by the following descriptor variables:
[B.1] High Nomination_SuccessRate
[B.2] High Nominations_Total
[B.3] Picture=WON
[B.4] Editing=WON
[B.5] Sound=WON
[B.6] Directing=WON
[B.7] Cinematography=WON
[B.7] Design=WON
[C] PC2 can be described as having won best picture as well as editing and sound awards, but with a few number of nominations but won directing, cinematography and design awards, as characterized by the following descriptor variables:
[C.1] High Nomination_SuccessRate with:
[C.1.1] Picture=WON
[C.1.2] Editing=WON
[C.1.3] Sound=WON
[C.2] Low Nominations_Total with:
[C.2.1] Directing=WON
[C.2.2] Cinematography=WON
[C.2.3] Design=WON
##################################
# Loading dataset
##################################
SD_MFA <- Oscars.MFA
str(SD_MFA)## 'data.frame': 126 obs. of 10 variables:
## $ Nominations_Total : int 9 2 4 3 9 8 6 2 5 6 ...
## $ Nomination_SuccessRate: num 0.333 0.5 0 0 0.667 ...
## $ Picture : Factor w/ 2 levels "NOM","WON": 1 1 1 1 2 1 1 1 1 1 ...
## $ Cinematography : Factor w/ 3 levels "NNOM","NOM","WON": 3 1 1 1 2 2 1 1 1 1 ...
## $ Directing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 1 1 3 2 2 1 1 2 ...
## $ Editing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 2 1 3 2 2 1 1 1 ...
## $ Screenplay : Factor w/ 3 levels "NNOM","NOM","WON": 1 1 2 2 3 2 3 2 2 2 ...
## $ Acting : Factor w/ 3 levels "NNOM","NOM","WON": 1 3 1 2 2 3 3 1 1 2 ...
## $ Design : Factor w/ 3 levels "NNOM","NOM","WON": 3 1 1 1 1 1 1 1 1 1 ...
## $ Sound : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 1 1 3 2 1 1 2 1 ...##################################
# Performing MFA
##################################
DR_MFA <- MFA(SD_MFA[,c(1:10)],
group=c(2,3,3,2),
type =c("s","n","n","n"),
name.group = c("Recognitions","Technicalities","Storytelling","Aesthetics"),
graph = FALSE)
##################################
# Obtaining the MFA eigenvalues
##################################
(DR_MFA_EV <- get_eigenvalue(DR_MFA))## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 2.390168e+00 2.060303e+01 20.60303
## Dim.2 1.521051e+00 1.311132e+01 33.71435
## Dim.3 1.424525e+00 1.227928e+01 45.99362
## Dim.4 9.027718e-01 7.781809e+00 53.77543
## Dim.5 8.101777e-01 6.983656e+00 60.75909
## Dim.6 7.757389e-01 6.686797e+00 67.44588
## Dim.7 6.798692e-01 5.860409e+00 73.30629
## Dim.8 6.685041e-01 5.762443e+00 79.06874
## Dim.9 4.857959e-01 4.187515e+00 83.25625
## Dim.10 4.463849e-01 3.847796e+00 87.10405
## Dim.11 4.185774e-01 3.608098e+00 90.71215
## Dim.12 3.160011e-01 2.723900e+00 93.43605
## Dim.13 2.367877e-01 2.041087e+00 95.47713
## Dim.14 1.938533e-01 1.670997e+00 97.14813
## Dim.15 1.405943e-01 1.211910e+00 98.36004
## Dim.16 1.217728e-01 1.049670e+00 99.40971
## Dim.17 6.847969e-02 5.902885e-01 100.00000
## Dim.18 2.546615e-31 2.195158e-30 100.00000
## Dim.19 8.932530e-32 7.699757e-31 100.00000
## Dim.20 7.111011e-32 6.129625e-31 100.00000
## Dim.21 5.620170e-32 4.844534e-31 100.00000
## Dim.22 5.068452e-32 4.368958e-31 100.00000
## Dim.23 2.045206e-32 1.762949e-31 100.00000
## Dim.24 1.643285e-32 1.416497e-31 100.00000
## Dim.25 5.361193e-34 4.621298e-33 100.00000##################################
# Formulating the Scree Plot
# for the variances
##################################
(DR_MFA_VarianceScreePlot <- fviz_eig(DR_MFA,
addlabels = TRUE,
ylim = c(0, 100),
choice = c("variance")) +
labs(title = "Multiple Factor Analysis : Scree Plot of Explained Variances",
subtitle = "Top 2 Principal Components",
y = "Percentage of Explained Variances",
x = "Principal Components") +
theme_classic())
##################################
# Formulating the Scree Plot
# for the eigenvalues
##################################
(DR_MFA_EigenvalueScreePlot <- fviz_eig(DR_MFA,
addlabels = TRUE,
ylim = c(0, 6),
choice = c("eigenvalue")) +
labs(title = "Multiple Factor Analysis : Scree Plot of Eigenvalues",
subtitle = "Top 2 Principal Components",
y = "Eigenvalues",
x = "Principal Components") +
theme_classic())
##################################
# Extracting the MFA
# descriptor variable loadings
##################################
DR_MFA_VAR <- get_mfa_var(DR_MFA)
##################################
# Extracting the coordinates
# representing the loadings
# for the descriptor variables
##################################
DR_MFA_VAR$coord## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Nominations_Total 0.8315040 -0.436788 0.1298438 -0.15550666 0.02120145
## Nomination_SuccessRate 0.6061531 0.687584 0.1110336 0.09400855 -0.21971319##################################
# Extracting the quality of representation
# for the descriptor variables
# on the factor map
##################################
DR_MFA_VAR$cos2## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Nominations_Total 0.6913990 0.1907837 0.01685940 0.024182322 0.0004495016
## Nomination_SuccessRate 0.3674216 0.4727718 0.01232846 0.008837607 0.0482738848##################################
# Extracting the contributions
# (in percentage) of the descriptor variables
# to the principal components
##################################
DR_MFA_VAR$contrib## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Nominations_Total 24.11964 10.45847 0.9868303 2.2335234 0.04626168
## Nomination_SuccessRate 12.81760 25.91661 0.7216212 0.8162575 4.96823865##################################
# Extracting the dimensions
# for the descriptor variables
# on the factor map
##################################
(DR_MFA_VariableGroups <- fviz_mfa_var(DR_MFA,
choice = "group") +
labs(title = "Multiple Factor Analysis : Factorial Map of Variable Groups",
subtitle = "Descriptor Variable Principal Components",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Extracting the dimensions
# for the qunatitative descriptor variables
# on the factor map
##################################
(DR_MFA_QuantitativeVariableGroups <- fviz_mfa_var(DR_MFA,
choice = "quanti.var") +
labs(title = "Multiple Factor Analysis : Correlation Plot of Quantitative Variables",
subtitle = "Quantitative Descriptor Variable Principal Components",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Graphing the individual instances
# from qualitative descriptor variables
# on the factor map
##################################
(DR_MFA_QualitativeIndividualGroups <- fviz_mfa_ind(DR_MFA,
partial = "all",
geom = "text",
repel = TRUE,
habillage = SD_MFA$Picture,
palette = c("#888888","#5544FF"),
legend.title = "Picture") +
labs(title = "Multiple Factor Analysis : Factorial Map of Individuals",
subtitle = "Qualitative Descriptor Variable Principal Components",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Extracting the dimensions
# for the qualitative descriptor variables
# on the factor map
##################################
(DR_MFA_QualitativeVariableGroups <- fviz_mfa_var(DR_MFA,
choice = "quali.var",
geom = "text") +
labs(title = "Multiple Factor Analysis : Factorial Map of Qualitative Variables",
subtitle = "Qualitative Descriptor Variable Principal Components",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Formulating the Biplot
# using the individual scores
# and qualitative descriptor variable loadings
# for the Top 1 and Top 2 principal components
##################################
Picture <- as.factor(SD_MFA[,"Picture"])
(DR_MCA_QualitativeBiplot <- fviz_mfa_quali_biplot(DR_MFA,
repel = TRUE,
geom = "text",
habillage = Picture,
palette = c("#888888","#5544FF"),
col.var = "#FF5050",
legend.title = "Picture") +
labs(title = "Multiple Factor Analysis : Biplot",
subtitle = "Individual Scores versus Qualitative Descriptor Variable Loadings",
x = "Principal Component 1",
y = "Principal Component 2") +
theme_classic() +
theme(legend.position="top"))
1.5.5 Factor Analysis of Mixed Data (FAMD)
Factor Analysis of Mixed Data reduces data dimensionality to identify nearness between both quantitative and qualitative variables, as well as the proximity between the observations by combining the Principal Component Analysis (PCA) and Multiple Correspondence Analysis (MCA). The method employs a series of statistical transformations, including calculations of the correlation matrix, eigenvalues and eigenvectors, on a set of qualitative and/or quantitative variables in order to project them on a vector space generated by orthogonal components.
[A] The percentage contributions for each principal component derived from the analysis in explaining the variance in the dataset are given as follows:
[A.1] PC1 = 54%
[A.2] Combined PC1 and PC2 = 82%
[A.3] Combined PC1, PC2 and PC3 = 100%
[B] With eigenvalues sufficiently greater than 1, only PC1 and PC2 were used in the subsequent exploratory analysis.
[B.1] PC1 = 1.60
[B.1] PC2 = 1.00
[C] PC1 can be described as having a higher number of awards won including best picture, as characterized by the following descriptor variables, ranked based on contribution and statistical significance:
[C.1] Picture=WON = 40.90%
[C.2] High Nomination_SuccessRate = 40.01%
[D] PC2 can be described a high number of oscar nominations, as characterized by the following descriptor variables, ranked based on importance and statistical significance:
[D.1] High Nominations_Total = 80.81%
[E] With both PC1 and PC2 considered,the following relationships were observed among descriptor variables:
[E.1] All descriptor variables were well-represented for both principal components.
[E.1.1] Picture
[E.1.2] Nomination_SuccessRate
[E.1.3] Nominations_Total
[E.2] Descriptor variables demonstrated correlation and clustered around two groups:
[E.2.1] Cluster 1 (Picture, Nomination_SuccessRate) indicates that best picture winners also won most awards.
[E.2.2] Cluster 2 (Nominations_Total) indicates that best picture nominees can have a high number of nominations without actually winning most awards including best picture.
[F] With both PC1 and PC2 considered,the following relationships were observed among individual instances:
[F.1] Best picture winners are also associated with winning for best screenplay (e.g. The Hurt Locker, The King’s Speech, Argo, 12 Years a Slave, Birdman or (The Unexpected Virtue of Ignorance), Spotlight, Moonlight, Green Book, Parasite, CODA, Everything Everywhere All at Once).
[F.2] Best picture winners are also associated with winning for best directing (e.g. The Hurt Locker, The King’s Speech, The Artist, Birdman or (The Unexpected Virtue of Ignorance), The Shape of Water, Parasite, Nomadland, Everything Everywhere All at Once).
[F.3] Best picture winners are not readily associated with winning for best editing or cinematography.
##################################
# Loading dataset
##################################
SD_FAMD <- Oscars.FAMD
str(SD_FAMD)## 'data.frame': 126 obs. of 7 variables:
## $ Nominations_Total : int 9 2 4 3 9 8 6 2 5 6 ...
## $ Nomination_SuccessRate: num 0.333 0.5 0 0 0.667 ...
## $ Picture : Factor w/ 2 levels "NOM","WON": 1 1 1 1 2 1 1 1 1 1 ...
## $ Cinematography : Factor w/ 3 levels "NNOM","NOM","WON": 3 1 1 1 2 2 1 1 1 1 ...
## $ Directing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 1 1 3 2 2 1 1 2 ...
## $ Editing : Factor w/ 3 levels "NNOM","NOM","WON": 2 1 2 1 3 2 2 1 1 1 ...
## $ Screenplay : Factor w/ 3 levels "NNOM","NOM","WON": 1 1 2 2 3 2 3 2 2 2 ...##################################
# Performing FAMD
##################################
DR_FAMD <- FAMD(SD_FAMD[,c(1:3)],
graph = FALSE)
##################################
# Obtaining the FAMD eigenvalues
##################################
(DR_FAMD_EV <- get_eigenvalue(DR_FAMD))## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 1.6055601 53.51867 53.51867
## Dim.2 0.8576607 28.58869 82.10736
## Dim.3 0.5367791 17.89264 100.00000##################################
# Formulating the Scree Plot
# for the variances
##################################
(DR_FAMD_VarianceScreePlot <- fviz_eig(DR_FAMD,
addlabels = TRUE,
ylim = c(0, 100),
choice = c("variance")) +
labs(title = "Factor Analysis of Mixed Data : Scree Plot of Explained Variances",
subtitle = "Top 2 Principal Components",
y = "Percentage of Explained Variances",
x = "Principal Components") +
theme_classic())
##################################
# Formulating the Scree Plot
# for the eigenvalues
##################################
(DR_FAMD_EigenvalueScreePlot <- fviz_eig(DR_FAMD,
addlabels = TRUE,
ylim = c(0, 6),
choice = c("eigenvalue")) +
labs(title = "Factor Analysis of Mixed Data : Scree Plot of Eigenvalues",
subtitle = "Top 2 Principal Components",
y = "Eigenvalues",
x = "Principal Components") +
theme_classic())
##################################
# Extracting the FAMD
# descriptor variable loadings
##################################
DR_FAMD_VAR <- get_famd_var(DR_FAMD)
##################################
# Extracting the coordinates
# representing the loadings
# for the descriptor variables
##################################
DR_FAMD_VAR$coord## Dim.1 Dim.2 Dim.3
## Nominations_Total 0.3063051 0.69312071 0.0005742175
## Nomination_SuccessRate 0.6424797 0.09498771 0.2625326094
## Picture 0.6567754 0.06955231 0.2736723010##################################
# Extracting the quality of representation
# for the descriptor variables
# on the factor map
##################################
DR_FAMD_VAR$cos2## Dim.1 Dim.2 Dim.3
## Nominations_Total 0.0938228 0.480416312 3.297257e-07
## Nomination_SuccessRate 0.4127801 0.009022666 6.892337e-02
## Picture 0.4313539 0.004837524 7.489653e-02##################################
# Extracting the contributions
# (in percentage) of the descriptor variables
# to the principal components
##################################
DR_FAMD_VAR$contrib## Dim.1 Dim.2 Dim.3
## Nominations_Total 19.07777 80.815255 0.1069746
## Nomination_SuccessRate 40.01592 11.075208 48.9088707
## Picture 40.90631 8.109537 50.9841547##################################
# Extracting the quality of representation
# for the descriptor variables
# on the factor map
##################################
(DR_FAMD_VariableSquaredCorrelationCircle <- fviz_famd_var(DR_FAMD,
col.var = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
legend.title = "Squared Coordinates") +
labs(title = "Factor Analysis of Mixed Data : Squared Coordinate Plot",
subtitle = "Descriptor Variable Representation Quality",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Formulating clusters of the
# descriptor variables
##################################
set.seed(123)
DR_FAMD_KMEANS <- kmeans(DR_FAMD_VAR$coord, centers=2, nstart=25)
DR_FAMD_KMEANS_CLUSTER <- as.factor(DR_FAMD_KMEANS$cluster)
##################################
# Extracting the correlation
# between the descriptor variables
# and top principal components
##################################
(DR_FAMD_VariableCorrelationCircle <- fviz_famd_var(DR_FAMD,
col.var = DR_FAMD_KMEANS_CLUSTER,
palette = c("#0073C2FF",
"#EFC000FF"),
legend.title = "Cluster") +
labs(title = "Factor Analysis of Mixed Data : Factorial Map of Quantitative and Qualitative Variables",
subtitle = "Principal Components Versus Descriptor Variable Clusters",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
##################################
# Extracting the contribution
# of the descriptor variables
# for the the Top 1 and 2 principal components
##################################
(DR_FAMD_PCVariableContributors <- fviz_contrib(DR_FAMD,
choice = "var",
axes = 1:2) +
labs(title = "Factor Analysis of Mixed Data : Descriptor Variable Contribution",
subtitle = "Principal Components 1 and 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Testing the statistical significance
# of the contribution
# of the descriptor variables
# for the the Top 1 and 2 principal components
##################################
DR_FAMD_VariableContributionTest <- dimdesc(DR_FAMD,
axes = c(1,2),
proba = 0.05)
##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 1 principal component
##################################
(DR_FAMD_PC1VariableContributors <- fviz_contrib(DR_FAMD,
choice = "var",
axes = 1) +
labs(title = "Factor Analysis of Mixed Data : Descriptor Variable Contribution",
subtitle = "Principal Component 1 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Testing the statistical significance
# of the contribution
# of the descriptor variables
# for the Top 1 principal component
##################################
DR_FAMD_VariableContributionTest$Dim.1##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## Nomination_SuccessRate 0.8015483 1.791314e-29
## Nominations_Total 0.5534484 1.803999e-11
##
## Link between the variable and the categorical variable (1-way anova)
## =============================================
## R2 p.value
## Picture 0.6567754 1.411641e-30
##
## Link between variable abd the categories of the categorical variables
## ================================================================
## Estimate p.value
## Picture=WON 1.633764 1.411641e-30
## Picture=NOM -1.633764 1.411641e-30##################################
# Extracting the contribution
# of the descriptor variables
# for the Top 2 principal component
##################################
(DR_FAMD_PC2VariableContributors <- fviz_contrib(DR_FAMD,
choice = "var",
axes = 2) +
labs(title = "Factor Analysis of Mixed Data : Descriptor Variable Contribution",
subtitle = "Principal Component 2 Contributors",
x = "Descriptors") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90,hjust = 1)))
##################################
# Testing the statistical significance
# of the contribution
# of the descriptor variables
# for the Top 2 principal component
##################################
DR_FAMD_VariableContributionTest$Dim.2##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## Nominations_Total 0.8325387 1.331762e-33
## Nomination_SuccessRate -0.3082008 4.465369e-04
##
## Link between the variable and the categorical variable (1-way anova)
## =============================================
## R2 p.value
## Picture 0.06955231 0.002846506
##
## Link between variable abd the categories of the categorical variables
## ================================================================
## Estimate p.value
## Picture=NOM 0.3885806 0.002846506
## Picture=WON -0.3885806 0.002846506##################################
# Extracting the FAMD individual scores
##################################
DR_FAMD_IND <- get_famd_ind(DR_FAMD)
##################################
# Extracting the coordinates
# representing the scores
# for the individuals
##################################
DR_FAMD_IND$coord[,c("Dim.1","Dim.2")]## Dim.1 Dim.2
## Avatar 0.477671939 0.78718319
## The Blind Side -0.172294892 -1.85825949
## District 9 -1.360047435 -0.37985738
## An Education -1.525188667 -0.71974737
## The Hurt Locker 3.524847885 -0.65138268
## Inglourious Basterds -0.319973758 0.78004709
## Precious: Based on the Novel 'Push' by Sapphire -0.017751755 -0.23248680
## A Serious Man -1.690329898 -1.05963737
## Up 0.019521801 -0.67886507
## Up in the Air -1.029764972 0.29992262
## Black Swan -0.587692201 -0.35941622
## The Fighter 0.002811822 0.18346397
## Inception 0.818552497 0.18108050
## The Kids Are All Right -1.360047435 -0.37985738
## The King's Speech 3.008228002 0.90071270
## 127 Hours -1.029764972 0.29992262
## The Social Network 0.439043745 0.38073603
## Toy Story 3 0.019521801 -0.67886507
## True Grit -0.369200046 1.65948261
## Winter's Bone -1.360047435 -0.37985738
## The Artist 3.183967328 -0.04527999
## The Descendants -0.587692201 -0.35941622
## Extremely Loud & Incredibly Close -1.690329898 -1.05963737
## The Help -0.601029932 -0.77916843
## Hugo 1.175986809 1.27334524
## Midnight in Paris -0.601029932 -0.77916843
## Moneyball -1.029764972 0.29992262
## The Tree of Life -1.525188667 -0.71974737
## War Horse -1.029764972 0.29992262
## Amour -0.587692201 -0.35941622
## Argo 2.471677152 -0.95085883
## Beasts of the Southern Wild -1.360047435 -0.37985738
## Django Unchained 0.019521801 -0.67886507
## Les Miserables 0.477671939 0.78718319
## Life of Pi 0.899977684 1.41855072
## Lincoln 0.467104206 2.07304991
## Silver Linings Playbook -0.319973758 0.78004709
## Zero Dark Thirty -0.587692201 -0.35941622
## American Hustle -0.369200046 1.65948261
## Captain Phillips -1.029764972 0.29992262
## Dallas Buyers Club 0.488270034 -0.49869950
## Gravity 1.756048962 0.54141165
## Her -0.587692201 -0.35941622
## Nebraska -1.029764972 0.29992262
## Philomena -1.360047435 -0.37985738
## 12 Years a Slave 2.512804307 -0.11895729
## The Wolf of Wall Street -1.194906204 -0.03996738
## American Sniper -0.523743184 0.03370992
## Birdman or (The Unexpected Virtue of Ignorance) 2.850142046 -0.29642710
## Boyhood -0.523743184 0.03370992
## The Grand Budapest Hotel 0.815009678 0.60971339
## The Imitation Game -0.319973758 0.78004709
## Selma -0.172294892 -1.85825949
## The Theory of Everything -0.587692201 -0.35941622
## Whiplash 0.626735803 -0.99831392
## The Big Short -0.587692201 -0.35941622
## Bridge of Spies -0.523743184 0.03370992
## Brooklyn -1.525188667 -0.71974737
## Mad Max: Fury Road 1.452441961 0.70113607
## The Martian -0.864623741 0.63981262
## The Revenant 0.720099920 1.93995155
## Room -0.601029932 -0.77916843
## Spotlight 2.017380613 -1.13862729
## Arrival -0.319973758 0.78004709
## Fences -0.601029932 -0.77916843
## Hacksaw Ridge -0.017751755 -0.23248680
## Hell or High Water -1.360047435 -0.37985738
## Hidden Figures -1.525188667 -0.71974737
## La La Land 1.592533405 2.33451164
## Lion -1.029764972 0.29992262
## Manchester by the Sea -0.017751755 -0.23248680
## Moonlight 2.474176113 -0.52540446
## Call Me by Your Name -0.601029932 -0.77916843
## Darkest Hour -0.017751755 -0.23248680
## Dunkirk 0.439043745 0.38073603
## Get Out -0.601029932 -0.77916843
## Lady Bird -1.194906204 -0.03996738
## Phantom Thread -0.523743184 0.03370992
## The Post -1.690329898 -1.05963737
## The Shape of Water 3.095524398 1.28155604
## Three Billboards outside Ebbing, Missouri 0.002811822 0.18346397
## Black Panther 0.436544784 -0.04471834
## BlacKkKlansman -0.523743184 0.03370992
## Bohemian Rhapsody 1.233949806 -1.31776276
## The Favourite -0.065593045 1.49975819
## Green Book 2.661868171 -1.90445440
## Roma 0.541620957 1.18030934
## A Star Is Born -0.319973758 0.78004709
## Vice -0.319973758 0.78004709
## Ford v Ferrari 0.157987571 -1.17847949
## The Irishman -0.369200046 1.65948261
## Jojo Rabbit -0.523743184 0.03370992
## Joker 0.347959435 1.70896166
## Little Women -0.523743184 0.03370992
## Marriage Story -0.523743184 0.03370992
## 1917 0.541620957 1.18030934
## Once upon a Time...in Hollywood 0.238013956 1.34003376
## Parasite 3.029424191 -1.67105268
## The Father -0.017751755 -0.23248680
## Judas and the Black Messiah -0.017751755 -0.23248680
## Mank 0.238013956 1.34003376
## Minari -0.523743184 0.03370992
## Nomadland 2.523402402 -1.40483998
## Promising Young Woman -0.587692201 -0.35941622
## Sound of Metal -0.017751755 -0.23248680
## The Trial of the Chicago 7 -1.029764972 0.29992262
## Belfast -0.430890779 0.41163031
## CODA 3.546013713 -3.22313209
## Don't Look Up -1.360047435 -0.37985738
## Drive My Car -0.601029932 -0.77916843
## Dune 1.452441961 0.70113607
## King Richard -0.523743184 0.03370992
## Licorice Pizza -1.525188667 -0.71974737
## Nightmare Alley -1.360047435 -0.37985738
## The Power of the Dog 0.214078131 2.20616424
## West Side Story -0.430890779 0.41163031
## All Quiet on the Western Front 0.815009678 0.60971339
## Avatar: The Way of Water -0.601029932 -0.77916843
## The Banshees of Inisherin -0.534341278 1.31959261
## Elvis -0.699482509 0.97970261
## Everything Everywhere All at Once 3.763107066 0.07680978
## The Fabelmans -0.864623741 0.63981262
## Tar -1.029764972 0.29992262
## Top Gun: Maverick -0.523743184 0.03370992
## Triangle of Sadness -1.525188667 -0.71974737
## Women Talking -0.172294892 -1.85825949##################################
# Extracting the quality of representation
# for the individuals
# on the factor map
##################################
DR_FAMD_IND$cos2[,c("Dim.1","Dim.2")]## Dim.1 Dim.2
## Avatar 1.872102e-01 0.5084187848
## The Blind Side 6.379316e-03 0.7420651260
## District 9 7.970443e-01 0.0621749536
## An Education 7.303059e-01 0.1626364356
## The Hurt Locker 9.451994e-01 0.0322786298
## Inglourious Basterds 1.419278e-01 0.8434908068
## Precious: Based on the Novel 'Push' by Sapphire 8.259804e-04 0.1416719048
## A Serious Man 6.590056e-01 0.2589766896
## Up 3.545355e-04 0.4287330112
## Up in the Air 7.316126e-01 0.0620616557
## Black Swan 7.090228e-01 0.2651891351
## The Fighter 3.696853e-05 0.1573830733
## Inception 3.285314e-01 0.0160778190
## The Kids Are All Right 7.970443e-01 0.0621749536
## The King's Speech 7.237137e-01 0.0648810458
## 127 Hours 7.316126e-01 0.0620616557
## The Social Network 2.189816e-01 0.1646796971
## Toy Story 3 3.545355e-04 0.4287330112
## True Grit 4.344373e-02 0.8777059345
## Winter's Bone 7.970443e-01 0.0621749536
## The Artist 8.947340e-01 0.0001809545
## The Descendants 7.090228e-01 0.2651891351
## Extremely Loud & Incredibly Close 6.590056e-01 0.2589766896
## The Help 3.473706e-01 0.5837992755
## Hugo 3.383463e-01 0.3966878352
## Midnight in Paris 3.473706e-01 0.5837992755
## Moneyball 7.316126e-01 0.0620616557
## The Tree of Life 7.303059e-01 0.1626364356
## War Horse 7.316126e-01 0.0620616557
## Amour 7.090228e-01 0.2651891351
## Argo 6.875993e-01 0.1017616166
## Beasts of the Southern Wild 7.970443e-01 0.0621749536
## Django Unchained 3.545355e-04 0.4287330112
## Les Miserables 1.872102e-01 0.5084187848
## Life of Pi 2.408257e-01 0.5983139173
## Lincoln 4.823662e-02 0.9500988669
## Silver Linings Playbook 1.419278e-01 0.8434908068
## Zero Dark Thirty 7.090228e-01 0.2651891351
## American Hustle 4.344373e-02 0.8777059345
## Captain Phillips 7.316126e-01 0.0620616557
## Dallas Buyers Club 1.349085e-01 0.1407333918
## Gravity 4.529955e-01 0.0430601812
## Her 7.090228e-01 0.2651891351
## Nebraska 7.316126e-01 0.0620616557
## Philomena 7.970443e-01 0.0621749536
## 12 Years a Slave 6.943401e-01 0.0015560984
## The Wolf of Wall Street 8.195722e-01 0.0009169189
## American Sniper 9.953032e-01 0.0041231976
## Birdman or (The Unexpected Virtue of Ignorance) 8.225854e-01 0.0088978236
## Boyhood 9.953032e-01 0.0041231976
## The Grand Budapest Hotel 3.320641e-01 0.1858436979
## The Imitation Game 1.419278e-01 0.8434908068
## Selma 6.379316e-03 0.7420651260
## The Theory of Everything 7.090228e-01 0.2651891351
## Whiplash 1.120504e-01 0.2843011476
## The Big Short 7.090228e-01 0.2651891351
## Bridge of Spies 9.953032e-01 0.0041231976
## Brooklyn 7.303059e-01 0.1626364356
## Mad Max: Fury Road 4.304396e-01 0.1003042290
## The Martian 5.182075e-01 0.2837624742
## The Revenant 1.174171e-01 0.8521726675
## Room 3.473706e-01 0.5837992755
## Spotlight 4.929227e-01 0.1570241106
## Arrival 1.419278e-01 0.8434908068
## Fences 3.473706e-01 0.5837992755
## Hacksaw Ridge 8.259804e-04 0.1416719048
## Hell or High Water 7.970443e-01 0.0621749536
## Hidden Figures 7.303059e-01 0.1626364356
## La La Land 2.828220e-01 0.6077545153
## Lion 7.316126e-01 0.0620616557
## Manchester by the Sea 8.259804e-04 0.1416719048
## Moonlight 6.991856e-01 0.0315296223
## Call Me by Your Name 3.473706e-01 0.5837992755
## Darkest Hour 8.259804e-04 0.1416719048
## Dunkirk 2.189816e-01 0.1646796971
## Get Out 3.473706e-01 0.5837992755
## Lady Bird 8.195722e-01 0.0009169189
## Phantom Thread 9.953032e-01 0.0041231976
## The Post 6.590056e-01 0.2589766896
## The Shape of Water 6.789594e-01 0.1163725546
## Three Billboards outside Ebbing, Missouri 3.696853e-05 0.1573830733
## Black Panther 1.887202e-01 0.0019803056
## BlacKkKlansman 9.953032e-01 0.0041231976
## Bohemian Rhapsody 1.957369e-01 0.2232298239
## The Favourite 1.887256e-03 0.9866376195
## Green Book 6.226013e-01 0.3186970691
## Roma 1.507362e-01 0.7158436701
## A Star Is Born 1.419278e-01 0.8434908068
## Vice 1.419278e-01 0.8434908068
## Ford v Ferrari 9.459975e-03 0.5263664507
## The Irishman 4.344373e-02 0.8777059345
## Jojo Rabbit 9.953032e-01 0.0041231976
## Joker 3.960200e-02 0.9552664219
## Little Women 9.953032e-01 0.0041231976
## Marriage Story 9.953032e-01 0.0041231976
## 1917 1.507362e-01 0.7158436701
## Once upon a Time...in Hollywood 3.009193e-02 0.9538424608
## Parasite 7.456688e-01 0.2268851430
## The Father 8.259804e-04 0.1416719048
## Judas and the Black Messiah 8.259804e-04 0.1416719048
## Mank 3.009193e-02 0.9538424608
## Minari 9.953032e-01 0.0041231976
## Nomadland 6.603859e-01 0.2046814563
## Promising Young Woman 7.090228e-01 0.2651891351
## Sound of Metal 8.259804e-04 0.1416719048
## The Trial of the Chicago 7 7.316126e-01 0.0620616557
## Belfast 5.184356e-01 0.4731241247
## CODA 5.416809e-01 0.4475266571
## Don't Look Up 7.970443e-01 0.0621749536
## Drive My Car 3.473706e-01 0.5837992755
## Dune 4.304396e-01 0.1003042290
## King Richard 9.953032e-01 0.0041231976
## Licorice Pizza 7.303059e-01 0.1626364356
## Nightmare Alley 7.970443e-01 0.0621749536
## The Power of the Dog 9.258054e-03 0.9832201697
## West Side Story 5.184356e-01 0.4731241247
## All Quiet on the Western Front 3.320641e-01 0.1858436979
## Avatar: The Way of Water 3.473706e-01 0.5837992755
## The Banshees of Inisherin 1.248614e-01 0.7615011681
## Elvis 2.841805e-01 0.5574796644
## Everything Everywhere All at Once 9.730857e-01 0.0004054068
## The Fabelmans 5.182075e-01 0.2837624742
## Tar 7.316126e-01 0.0620616557
## Top Gun: Maverick 9.953032e-01 0.0041231976
## Triangle of Sadness 7.303059e-01 0.1626364356
## Women Talking 6.379316e-03 0.7420651260##################################
# Extracting the contributions
# (in percentage) of the individuals
# to the principal components
##################################
DR_FAMD_IND$contrib[,c("Dim.1","Dim.2")]## Dim.1 Dim.2
## Avatar 1.127879e-01 0.573410388
## The Blind Side 1.467397e-02 3.195410419
## District 9 9.143469e-01 0.133522686
## An Education 1.149873e+00 0.479373595
## The Hurt Locker 6.141630e+00 0.392632593
## Inglourious Basterds 5.060945e-02 0.563061155
## Precious: Based on the Novel 'Push' by Sapphire 1.557706e-04 0.050016181
## A Serious Man 1.412361e+00 1.039030902
## Up 1.883834e-04 0.426462508
## Up in the Air 5.241784e-01 0.083240057
## Black Swan 1.707272e-01 0.119538909
## The Fighter 3.908216e-06 0.031146948
## Inception 3.312043e-01 0.030342915
## The Kids Are All Right 9.143469e-01 0.133522686
## The King's Speech 4.473262e+00 0.750734722
## 127 Hours 5.241784e-01 0.083240057
## The Social Network 9.528367e-02 0.134141105
## Toy Story 3 1.883834e-04 0.426462508
## True Grit 6.737928e-02 2.548351559
## Winter's Bone 9.143469e-01 0.133522686
## The Artist 5.011181e+00 0.001897259
## The Descendants 1.707272e-01 0.119538909
## Extremely Loud & Incredibly Close 1.412361e+00 1.039030902
## The Help 1.785645e-01 0.561793396
## Hugo 6.836090e-01 1.500397289
## Midnight in Paris 1.785645e-01 0.561793396
## Moneyball 5.241784e-01 0.083240057
## The Tree of Life 1.149873e+00 0.479373595
## War Horse 5.241784e-01 0.083240057
## Amour 1.707272e-01 0.119538909
## Argo 3.019857e+00 0.836654240
## Beasts of the Southern Wild 9.143469e-01 0.133522686
## Django Unchained 1.883834e-04 0.426462508
## Les Miserables 1.127879e-01 0.573410388
## Life of Pi 4.003745e-01 1.862102849
## Lincoln 1.078526e-01 3.976797215
## Silver Linings Playbook 5.060945e-02 0.563061155
## Zero Dark Thirty 1.707272e-01 0.119538909
## American Hustle 6.737928e-02 2.548351559
## Captain Phillips 5.241784e-01 0.083240057
## Dallas Buyers Club 1.178482e-01 0.230139830
## Gravity 1.524320e+00 0.271249611
## Her 1.707272e-01 0.119538909
## Nebraska 5.241784e-01 0.083240057
## Philomena 9.143469e-01 0.133522686
## 12 Years a Slave 3.121190e+00 0.013094716
## The Wolf of Wall Street 7.057819e-01 0.001478173
## American Sniper 1.355937e-01 0.001051549
## Birdman or (The Unexpected Virtue of Ignorance) 4.015465e+00 0.081311082
## Boyhood 1.355937e-01 0.001051549
## The Grand Budapest Hotel 3.283435e-01 0.344005504
## The Imitation Game 5.060945e-02 0.563061155
## Selma 1.467397e-02 3.195410419
## The Theory of Everything 1.707272e-01 0.119538909
## Whiplash 1.941654e-01 0.922248972
## The Big Short 1.707272e-01 0.119538909
## Bridge of Spies 1.355937e-01 0.001051549
## Brooklyn 1.149873e+00 0.479373595
## Mad Max: Fury Road 1.042799e+00 0.454902741
## The Martian 3.695364e-01 0.378808337
## The Revenant 2.563235e-01 3.482536655
## Room 1.785645e-01 0.561793396
## Spotlight 2.011771e+00 1.199712279
## Arrival 5.060945e-02 0.563061155
## Fences 1.785645e-01 0.561793396
## Hacksaw Ridge 1.557706e-04 0.050016181
## Hell or High Water 9.143469e-01 0.133522686
## Hidden Figures 1.149873e+00 0.479373595
## La La Land 1.253661e+00 5.043197985
## Lion 5.241784e-01 0.083240057
## Manchester by the Sea 1.557706e-04 0.050016181
## Moonlight 3.025966e+00 0.255447370
## Call Me by Your Name 1.785645e-01 0.561793396
## Darkest Hour 1.557706e-04 0.050016181
## Dunkirk 9.528367e-02 0.134141105
## Get Out 1.785645e-01 0.561793396
## Lady Bird 7.057819e-01 0.001478173
## Phantom Thread 1.355937e-01 0.001051549
## The Post 1.412361e+00 1.039030902
## The Shape of Water 4.736650e+00 1.519809425
## Three Billboards outside Ebbing, Missouri 3.908216e-06 0.031146948
## Black Panther 9.420208e-02 0.001850484
## BlacKkKlansman 1.355937e-01 0.001051549
## Bohemian Rhapsody 7.526583e-01 1.606898299
## The Favourite 2.126760e-03 2.081404132
## Green Book 3.502482e+00 3.356256064
## Roma 1.450086e-01 1.289156428
## A Star Is Born 5.060945e-02 0.563061155
## Vice 5.060945e-02 0.563061155
## Ford v Ferrari 1.233811e-02 1.285162331
## The Irishman 6.737928e-02 2.548351559
## Jojo Rabbit 1.355937e-01 0.001051549
## Joker 5.984944e-02 2.702580071
## Little Women 1.355937e-01 0.001051549
## Marriage Story 1.355937e-01 0.001051549
## 1917 1.450086e-01 1.289156428
## Once upon a Time...in Hollywood 2.800320e-02 1.661672422
## Parasite 4.536522e+00 2.584010124
## The Father 1.557706e-04 0.050016181
## Judas and the Black Messiah 1.557706e-04 0.050016181
## Mank 2.800320e-02 1.661672422
## Minari 1.355937e-01 0.001051549
## Nomadland 3.147574e+00 1.826281195
## Promising Young Woman 1.707272e-01 0.119538909
## Sound of Metal 1.557706e-04 0.050016181
## The Trial of the Chicago 7 5.241784e-01 0.083240057
## Belfast 9.177772e-02 0.156793702
## CODA 6.215609e+00 9.613247808
## Don't Look Up 9.143469e-01 0.133522686
## Drive My Car 1.785645e-01 0.561793396
## Dune 1.042799e+00 0.454902741
## King Richard 1.355937e-01 0.001051549
## Licorice Pizza 1.149873e+00 0.479373595
## Nightmare Alley 9.143469e-01 0.133522686
## The Power of the Dog 2.265414e-02 4.503909058
## West Side Story 9.177772e-02 0.156793702
## All Quiet on the Western Front 3.283435e-01 0.344005504
## Avatar: The Way of Water 1.785645e-01 0.561793396
## The Banshees of Inisherin 1.411368e-01 1.611364088
## Elvis 2.418558e-01 0.888183014
## Everything Everywhere All at Once 6.999968e+00 0.005459426
## The Fabelmans 3.695364e-01 0.378808337
## Tar 5.241784e-01 0.083240057
## Top Gun: Maverick 1.355937e-01 0.001051549
## Triangle of Sadness 1.149873e+00 0.479373595
## Women Talking 1.467397e-02 3.195410419##################################
# Extracting the correlation
# between the individual instances
# and top principal components
# for the qualitative descriptor variable
##################################
(DR_FAMD_IndividualFAMDGraphQualitativeVariable <- fviz_famd_ind(DR_FAMD,
geom.ind = "text",
col.ind = SD_FAMD$Cinematography,
palette = c("#888888","#5544FF","#F18EDE"),
repel = TRUE,
col.quali.var = "#FF0000",
legend.title = "Cinematography",
addEllipses = FALSE) +
labs(title = "Factor Analysis of Mixed Data : Factorial Map of Individuals (Cinematography)",
subtitle = "Individuals by Qualitative Descriptor Variable Principal Components",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
(DR_FAMD_IndividualFAMDGraphQualitativeVariable <- fviz_famd_ind(DR_FAMD,
geom.ind = "text",
col.ind = SD_FAMD$Directing,
palette = c("#888888","#5544FF","#F18EDE"),
repel = TRUE,
col.quali.var = "#FF0000",
legend.title = "Directing",
addEllipses = FALSE) +
labs(title = "Factor Analysis of Mixed Data : Factorial Map of Individuals (Directing)",
subtitle = "Individuals by Qualitative Descriptor Variable Principal Components",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
(DR_FAMD_IndividualFAMDGraphQualitativeVariable <- fviz_famd_ind(DR_FAMD,
geom.ind = "text",
col.ind = SD_FAMD$Editing,
palette = c("#888888","#5544FF","#F18EDE"),
repel = TRUE,
col.quali.var = "#FF0000",
legend.title = "Editing",
addEllipses = FALSE) +
labs(title = "Factor Analysis of Mixed Data : Factorial Map of Individuals (Editing)",
subtitle = "Individuals by Qualitative Descriptor Variable Principal Components",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
(DR_FAMD_IndividualFAMDGraphQualitativeVariable <- fviz_famd_ind(DR_FAMD,
geom.ind = "text",
col.ind = SD_FAMD$Screenplay,
palette = c("#888888","#5544FF","#F18EDE"),
repel = TRUE,
col.quali.var = "#FF0000",
legend.title = "Screenplay",
addEllipses = FALSE) +
labs(title = "Factor Analysis of Mixed Data : Factorial Map of Individuals (Screenplay)",
subtitle = "Individuals by Qualitative Descriptor Variable Principal Components",
y = "Principal Component 2",
x = "Principal Component 1") +
theme_classic() +
theme(legend.position="top"))
1.6 Algorithm Comparison Summary
2. References
[Book] Multiple Factor Analysis by Example Using R by Jerome Pages
[Book] Nonlinear Principal Component Analysis and Its Applications by Yuichi Mori, Masahiro Kuroda and Naomichi Makino
[Book] Applied Predictive Modeling by Max Kuhn and Kjell Johnson
[Book] An Introduction to Statistical Learning by Gareth James, Daniela Witten, Trevor Hastie and Rob Tibshirani
[Book] Multivariate Data Visualization with R by Deepayan Sarkar
[Book] Machine Learning by Samuel Jackson
[Book] Data Modeling Methods by Jacob Larget
[Book] Introduction to R and Statistics by University of Western Australia
[Book] Feature Engineering and Selection: A Practical Approach for Predictive Models by Max Kuhn and Kjell Johnson
[Book] Introduction to Research Methods by Eric van Holm
[R Package] AppliedPredictiveModeling by Max Kuhn
[R Package] caret by Max Kuhn
[R Package] rpart by Terry Therneau and Beth Atkinson
[R Package] lattice by Deepayan Sarkar
[R Package] dplyr by Hadley Wickham
[R Package] moments by Lukasz Komsta and Frederick
[R Package] skimr by Elin Waring
[R Package] RANN by Sunil Arya, David Mount, Samuel Kemp and Gregory Jefferis
[R Package] corrplot by Taiyun Wei
[R Package] tidyverse by Hadley Wickham
[R Package] lares by Bernardo Lares
[R Package] DMwR by Luis Torgo
[R Package] gridExtra by Baptiste Auguie and Anton Antonov
[R Package] rattle by Graham Williams
[R Package] RColorBrewer by Erich Neuwirth
[R Package] stats by R Core Team
[R Package] factoextra by Alboukadel Kassambara and Fabian Mundt
[R Package] FactoMineR by Francois Husson, Julie Josse, Sebastien Le and Jeremy Mazet
[Article] 6 Dimensionality Reduction Techniques in R (with Examples) by CMDLineTips Team
[Article] 6 Dimensionality Reduction Algorithms With Python by Jason Brownlee
[Article] Introduction to Dimensionality Reduction for Machine Learning by Jason Brownlee
[Article] Introduction to Dimensionality Reduction by Geeks For Geeks
[Article] Principal Component Analysis for Dimensionality Reduction in Python by Jason Brownlee
[Article] Principal Component Analysis Explained Simply by Linh Ngo
[Article] A Step-by-Step Explanation of Principal Component Analysis (PCA) by Zakaria Jaadi
[Article] What Is Principal Component Analysis (PCA) and How It Is Used? by Sartorius Team
[Article] Principal Components Analysis by Penn State Eberly College of Science
[Article] Principal Component Analysis – How PCA Algorithms Works, The Concept, Math and Implementation by Selva Prabhakaran
[Article] How Correspondence Analysis Works (A Simple Explanation) by Tim Bock
[Article] Understanding Correspondence Analysis: A Comprehensive Guide for 2023 by Matilda Sarah
[Article] Correspondence Analysis: What is it, and how can I use it to measure my Brand? (Part 1 of 2) by Qualtrics Team
[Article] Correspondence Analysis: What is it, and how can I use it to measure my Brand? (Part 2 of 2) by Qualtrics Team
[Article] Correspondence Analysis Explained by Everything Explained Today Team
[Article] Correspondence Analysis by IBM Team
[Article] Understanding and Applying Correspondence Analysis by Maarit Widmann and Alfredo Roccato
[Article] Correspondence Analysis by IBM Team
[Article] Multiple Correspondence Analysis (MCA) by XLSTAT Team
[Article] Multiple Correspondence Analysis by IBM Team
[Article] Multiple Factor Analysis (MFA) by XLSTAT Team
[Article] FAMD - Factor Analysis of Mixed Data in R: Essentials by Alboukadel Kassambara
[Article] Factor Analysis of Mixed Data Explained by Everything Explained Today Team
[Article] Factor Analysis of Mixed Data by Nancy Chelaru
[Article] Factorial Analysis of Mixed Data by XLSTAT Team
[Article] Factor Analysis of Mixed Data by Sohel Mahmood
[Article] FAMD: How To Generalize PCA to Categorical and Numerical Data by William Blaufuks
[Publication] Analysis of a Complex of Statistical Variables into Principal Components by Harold Hotelling (Journal of Educational Psychology)
[Publication] A Connection between Correlation and Contingency by Herman Hartley Hirschfeld (Mathematical Proceedings of the Cambridge Philosophical Society)
[Publication] Mixed Data for Factor Analysis by Jerome Pages (Journal of Applied Statistics)
[Course] Applied Data Mining and Statistical Learning by Penn State Eberly College of Science